the problem solution approach

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Article Contents

1. the problem-solution approach, 2. the ‘closest’ prior art, 3. the skilled person, 4. the ‘objective’ technical problem, 5. what happens when, 6. the objective ‘technical’ problem, 7. the problem-solution approach revisited.

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The problem-solution approach revisited

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Martin Müller, The problem-solution approach revisited, Journal of Intellectual Property Law & Practice , Volume 17, Issue 2, February 2022, Pages 199–209, https://doi.org/10.1093/jiplp/jpab184

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Martin Müller, Dr.-Ing., Dipl.-Inform., is Chair of Technical Board of Appeal 3.5.06 and Member of the Enlarged Board of Appeal of the EPO.

This article

At the European Patent Office, inventive step is assessed according to the problem-solution approach. While well-established, some of its parameters remain controversial. This paper looks at some of them in view of the question of how convincing the resulting ‘story’ will be.

The author takes the view that a convincing story consistent with the problem-solution approach—and, more importantly, with Article 56 EPC—can be told with almost any ‘closest prior art’, ‘skilled person’ and ‘objective technical problem’, but only if due regard is given to what would have actually happened. Accordingly, it may not be necessary to discuss the parameters of the problem-solution approach in a dogmatic manner.

From this perspective, the problem-solution approach provides good—and well-tested—heuristics for selecting the ‘closest prior art’, determining the ‘skilled person’ and defining the ‘objective technical problem’. Also, as the problem-solution approach proposes a story with many details, and because each of them can come under separate scrutiny by the parties, a corresponding inventive-step objection has a good chance of being eventually accepted by them.

At the European Patent Office (EPO), the inventive-step requirement for the patentable invention is almost invariably assessed on the basis of what is called the problem-solution approach (PSA). While it may not quite be for the EPO what the Lord’s prayer is for Christians, 1 it certainly plays an eminent role in patent examination. All parties to the proceedings before the EPO, and the EPO departments themselves, 2 are at least encouraged—but actually expected—to present their cases in terms of this ‘master story’. 3 Developed by the Boards of Appeal of the EPO in their early years, 4 the PSA has become one of the most appreciated features of EPO decision-making for its relative predictability when it comes to the notoriously difficult appreciation of inventive step and as ‘a powerful communication tool to get an argument across’. 5

While there is broad agreement that the PSA is to be applied, there is still a degree of controversy as regards the details. This article is meant to touch upon some of these details and give the author’s personal opinion on the matter. 6

According to Article 52(1) EPC, European patents shall be granted for any inventions that, inter alia , involve an inventive step. Article 56 EPC provides that an invention shall be considered as involving an inventive step if, having regard to the state of the art, it is not obvious to a person skilled in the art. The state of the art is, according to Article 54(2) EPC, held to comprise everything made available to the public by means of a written or oral description, by use or in any other way before the date of filing of the European patent application. Rule 42(1)(c) EPC 7 stipulates that the description shall disclose the invention, as claimed, in such terms that the technical problem and its solution can be understood.

Per se , the EPC provides precious little guidance on how the inventive-step requirement is to be assessed or how a decision in this regard is to be reasoned. It is noteworthy though that Article 56 EPC defines inventive step by a negative. Any finding that the invention was obvious will lead to the conclusion that the invention does not involve an inventive step. Inversely, only if the invention cannot be found to be obvious will the invention be considered to involve an inventive step.

The author shares the premise expressed by Rees 8 that the arguments exchanged in patent examination as to why an invention is or is not inventive represent stories about the person skilled in the art (the ‘skilled person’) making an invention or failing to make it. 9 Moreover, the author finds appealing the idea that Article 56 EPC is a regulation that even demands such a story. 10 This idea will, however, not be pursued further below because it is a matter of fact that the PSA provides a master story that frames the inventive-step assessment at the EPO.

The provisions cited above set the stage for a story about inventive step. Its protagonist and only animate character 11 is the person skilled in the art. Another ‘character’, the invention, is inanimate. We know nothing about the invention other than that it involves the solution to a technical problem. 12 The skilled person is equipped with the state of the art as requisites. And the plot of the story is the question of whether the skilled person, having regard to the state of the art, would have found the invention obvious at the relevant date. 13

According to the Guidelines for Examination in the EPO (Guidelines or GL), 14 the PSA consists of three main stages, namely

determining the ‘closest prior art’, 15

establishing the ‘objective technical problem’ to be solved and

considering whether or not the claimed invention, starting from the ‘closest prior art’ and the ‘objective technical problem’, would have been obvious to the skilled person.

The ‘closest prior art’ (CPA) is a single piece of prior art, which is particularly similar to the claimed invention. 16 Typically, it is a printed document or a single embodiment within a document, but it may also be a public prior use or unwritten ‘common general knowledge in the art’; that is, anything belonging to the state of the art within the meaning of Article 54(2) EPC. 17 The ‘objective technical problem’ (OTP) is one which the skilled person is supposed to address starting from the ‘closest prior art’. 18 In a nutshell, it is formulated as how to achieve the technical effects of those features that distinguish the claimed invention from the CPA (henceforth also referred to as the ‘distinguishing features’), where, in order to avoid ex post   facto reasoning, the OTP must be formulated in such a way as not to contain any pointers to the (technical) features of the solution. 19

The PSA in this most general form leaves a number of central questions open, such as: Who is the pertinent skilled person and which competencies can be expected of them? What is ‘the art’ in which they are skilled? How exhaustive is the state of the art? How is the ‘closest prior art’ determined? In what sense must—and can—the ‘closest prior art’ be ‘closer’ than other pieces of prior art? Who selects the skilled person and the ‘closest prior art’, and in which order? What is ‘objective’ in the ‘objective technical problem’, and how can it be ensured that only ‘technical’ problems qualify? These questions are considered in more detail in the following sections.

Of course, there is case law of the Boards of Appeal on the mentioned questions but, on some of them, there is still a degree of controversy. It must be stressed that this paper expresses exclusively the author’s personal opinion, which may or may not correspond to part of this case law and which does not in any way pre-empt the future decision-making of the Boards of Appeal.

The PSA provides an interpretation of the inventive-step requirement according to Article 56 EPC but is not per se a legal requirement of the EPC. 20 In an early decision of the Boards of Appeal, it was stated that the ‘problem and solution approach’ is no more than one possible route for the assessment of inventiveness and that, accordingly, its use is not a sine qua non when deciding inventiveness under Article 56 EPC. 21 Although this is undeniably true, no decision of the Boards of Appeal has put forward an alternative systematic way of assessing inventive step. 22 In any case, any application of the PSA must at least be consistent with Article 56 EPC (and the other pertinent requirements of the EPC). Beyond that, the author believes that some of the questions cannot be answered dogmatically but should be judged according to how convincing the story on inventive step turns out to be. For, an applicant will more easily accept the refusal of a patent application (or a proprietor the revocation or an opponent the maintenance of a patent) if the reasoning sets out a scenario that they can accept as one which ‘could have happened in real life to a skilled person’. 23 Notably, the PSA ‘story’ is regularly different from what has actually happened when the real inventor conceived the invention. This reflects the idea that the patentability of an invention should not depend on how much effort inventors have put into their invention, if any, 24 but on any verifiable contribution the invention makes to the prior art.

Occasionally, it is a matter of discussion whether an individual story complies with what is perceived to be the ‘essence of the PSA’. 25 In such cases, the author would like to suggest that a degree of flexibility may be taken to satisfy the dictum of T465/92 that the EPC does not force the inventive-step assessment into a strict scheme.

In the following, a closer look is given to the notions of the ‘closest prior art’, the ‘skilled person’ and the ‘objective technical problem’, always in relation to the PSA. 26 In a separate section, consideration is given to the formulation of the ‘objective technical problem’ in the context of so-called ‘mixed inventions’, that is, inventions that are composed of technical and non-technical features, typically ‘computer-implemented inventions’. After all actors and requisites of the PSA have been introduced, it is considered to what degree it matters in which order they appear on stage. A summarizing section follows.

In the available state of the art, one piece of prior art may well stand out as being particularly ‘close’ to the invention, which may, therefore, be dubbed the ‘closest’ prior art. If that is the case, it is a matter of economy to assess inventive step starting from this CPA. It should be simpler to find a lack of inventive step from a piece of prior art ‘close’ to the invention than from a more remote one and, conversely, if the invention is non-obvious from the ‘closest’ prior art, it stands to reason that it will also, a fortiori , be non-obvious over more ‘remote’ prior art. 27 An idea of the CPA also is to encourage an opponent to present its strongest case first. 28

A problem here, apparently, is that there is no easy way to assess ‘closeness’ of prior art to the invention. In other words, there is no ‘metric’ between pieces of prior art or their disclosure. As a heuristic, the following criteria have been used: the CPA should be chosen to have a similar use and to require the minimum of structural and functional modifications. 29 Normally, preference is given to a piece of prior art in the same field of the invention and concerned with the same problem as the invention. 30 Both criteria are easy to justify. It is often more plausible that the skilled person would consider further improving a known use or purpose in the prior art than putting a known teaching to a different use. 31 In fact, finding an entirely new use for a known teaching, maybe even in a different field of technology, may well indicate an inventive step. And starting from a teaching that shares more features with the invention, fewer differences have to be addressed to assess obviousness. Alternatively, the CPA has been characterized as the ‘most promising springboard to the invention’. 32 Regularly, however, it is difficult to select a piece of prior art as ‘most promising’ without actually developing an inventive-step argument on its basis (as we all know, promises may be broken but also positive surprises are possible).

Randl nicely illustrated this dilemma with a mountaineering metaphor 33 in which the invention becomes the summit of a mountain, the prior art a number of base camps and the skilled person a mountaineer faced with the problem of reaching the summit without climbing (ie, without ‘inventive step’). In this situation it may happen that from a very close base camp, the summit cannot be reached because it requires climbing the ‘deadly north face’, whereas from a different base camp, a longer path leads to the summit without the need to climb. The summit thus is reachable without climbing (the invention is obvious) but not from the ‘closest’ base camp.

In view of this dilemma, it has been argued that all ‘feasible’ or ‘suitable’ starting points towards the invention had to be considered under the PSA. 34 Beyond that, some boards have expressed the idea that the PSA can, in principle, be based on any piece of prior art, irrespective of its closeness, suitability or feasibility. 35 If it could be shown that the skilled person would have found the invention obvious over any such prior art, the choice would not need any particular justification. 36 Also, giving up an inventive-step objection just because a ‘closer’ prior art becomes available would be in plain contradiction with Article 56 EPC. 37 If a prior art is so ‘remote’ from the invention as to appear ‘unsuitable’, it should be possible to argue that the skilled person would not conceivably have modified it so as to arrive at the claimed invention. 38

From day 1, the PSA was criticized as being based on hindsight because the CPA (and, in fact, the OTP, see Section 4 below) was chosen ex post facto in knowledge of the invention. 39 While this is factually true, this situation is unavoidable. Not only the CPA but all prior art is produced, by the EPO or an opponent, on the basis—that is, in the knowledge—of the patent application as filed in order to assess the patentability requirements. 40 Obviously, the risk of hindsight judgment is a real one. 41 However, it is a primary object of the PSA to reduce the risk of hindsight by providing an inventive-step decision in terms of several intermediate decisions, all of which are put up for discussion and may be separately challenged (see also Section 7 below).

More specifically, it can be (and is) discussed with the parties to EPO proceedings whether the skilled person, starting from a piece of prior art, would have had the occasion to address a particular problem or whether they would not. If not, the problem may have to be reformulated (see also Section 4 below). If no reasonable problem can be determined, the prior art could be dismissed as effectively ‘unsuitable’.

To the author, providing a justification for the selection of a starting point(s) on which a detailed inventive-step analysis is based is rather less important than justifying why an ‘attack’ based on documents found not to be closest, suitable or feasible is not heard or examined in detail 42 . For instance, if the opposition division hears or examines only some inventive-step ‘attacks’ raised by an opponent on the basis of different starting points, the fundamental right(s) to be heard under Article 113(1) EPC and to a properly reasoned decision would require a justification by the opposition division as to why some of these attacks are not examined in detail, in particular if an agreement amongst the parties on which starting point is the best or ‘closest’ piece of prior art cannot be reached. In that case, either all attacks need to be considered 43 or it must be argued why an attack can be (convincingly) predicted to fail to show obviousness if another one, based on the CPA, has failed. A concept of relative ‘closeness’ of the starting points to the claimed invention can be helpful here.

On a different issue, the author does not agree with the idea that it is the skilled person who selects the CPA and certainly not ‘in order to’ arrive at the claimed invention. In order to avoid hindsight reasoning, the skilled person cannot be assumed to know the invention when they become active and clearly do not act in an attempt to re-produce the claimed invention. It is the deciding body, be it an examining or opposition division or a Board of Appeal, which, when assessing the prior art in order to decide upon the obviousness of the claimed invention, may decide to consider a particular document to be the CPA—and, only in this sense, be said to ‘select’ the CPA—, but it cannot be the skilled person who, in order to make the invention, ‘selects’ the CPA. 44

The skilled person is a not a real person. It is a fictional character like many others to be found in the law such as the hypothetical ordinary and reasonable man, 45 the reasonably well-informed, reasonably observant and circumspect average customer, 46 the man in the street 47 and many others. 48 Such characters are referred to in judicial reasoning in an attempt to capture a reasonably realistic, albeit hypothetical, situation.

The skilled person in patent law is generally assumed to have an average skill in the art, that is, the skilled person is neither new to the field, in which case they might find everything non-obvious, nor a Nobel laureate, 49 to whom everything might appear obvious. The skilled person is not to be confused with the actual examiner or board member entrusted with the examination of a case. 50 Further properties of the skilled person have been considered in case law. 51 The skilled person does not know but has access to the entire state of the art and has little imagination or creativity 52 but is capable of routine experimentation 53 and will be using the basic skills of their trade. The skilled person was characterized as a nerd, boring 54 and forgetful 55 and as conservative in attitude. 56 Even the skilled person’s nationality and language competency were considered but found to be irrelevant. 57 In some cases, it was found that the skilled person should rather be conceived as a team of experts from different fields, if different partial problems (see Section 4 ) required persons with different skills for their solution 58 or if it was implausible that a single person would combine all the necessary competencies. 59 The author thinks that the effort of construing the ‘skilled person’ as a team rather than ascribing all necessary competencies to a single person is only justified by the desire to tell a plausible or ‘realistic’ story.

Inventive step is assessed with reference to what the skilled person would have found obvious. Apart from Article 56 EPC, the skilled person features only in two other requirements of the EPC. First, in Article 83 EPC and, correspondingly, Articles 100(b) and 138(1)(b) and Rule 31 EPC, which require the European application or patent to disclose the invention in a manner sufficiently clear and complete for it to be carried out by a person skilled in the art. Second, in the Protocol on the Interpretation of Article 69 EPC, which provides that the extent of protection conferred by a European patent is to be determined, if only in part, in view of what, from a consideration of the description and drawings by a person skilled in the art, the proprietor may have contemplated. Furthermore, case law has developed the understanding that it is for the skilled person to interpret the claims, with a ‘mind willing to understand’, not one ‘desirous of misunderstanding’. 60

The skilled person thus has (at least) two distinct functions in the framework of the EPC. When given the application or the patent as a whole, the skilled person is relied upon to determine the scope of the claims, the extent of protection and the sufficiency of disclosure. When given only the prior art, the skilled person is referred to in order to assess whether the claimed invention would have been obvious. These tasks are fundamentally different. So much so that it appears to have become common ground that it is more appropriate to talk about two different skilled persons 61 . One must have knowledge of the application as a whole and all necessary skills to construe and practice the invention. If, for example, the invention is in the field of bio-informatics, the skilled person (for sufficiency and claim construction) must be assumed to have the necessary skill in biology or life sciences and in computer science to be able to carry out the invention. 62 The skilled person for inventive step must have (or be able to gather) the knowledge necessary to understand the ‘closest prior art’ and to address the ‘objective technical problem’. Unless the CPA is already addressed to a reader skilled in both fields, it may be more appropriate to assume, as the skilled person, an expert in just one of the two fields who may or may not consult with experts of a different field. Once an ‘interdisciplinary’ field of technology has become established, it may be less controversial to assume a skilled person with skills in several disciplines. That said, it is also accepted that the level of skill for both tasks must be assumed to be the same. Sloppily speaking, this means that, for one and the same case, there cannot be an Article-56-moron and an Article-83-genius, as representatives of the applicant or proprietor are known to argue (nor, of course, vice versa). 63 In the rest of this article, only the skilled person with respect to Article 56 EPC is considered.

The question arises as to the ‘art’ in which the person skilled in the art must be assumed to be skilled. A priori , there are different possibilities. The ‘art’ might be the one needed to understand the application and the problem formulated in the application itself. It might be the art required to understand the CPA. It might be the art necessary to appreciate and address the OTP. Or it might be any combination of them, that is, the application, the CPA and the OTP. Generally, the author concurs with those saying that the skilled person must be qualified to address—albeit not necessarily to solve—the established OTP. 64

At the same time, the author takes the view that, as a matter of principle, almost any person could be considered to take the role of skilled person in the inventive-step story we tell. If an invention turned out to be obvious for a person of average skill in any particular art and from any particular piece of prior art which this person might come across, it would appear that the invention would have to be found to be obvious within the meaning of Article 56 EPC. For example, if a given invention were obvious for the man in the street having regard to the daily paper, for the man in the street and a paper on quantum computing, a computer scientist having contact with a notary’s workflow, 65 for a physicist and a brochure about a new smart phone or for a specialist in medical imaging and a white paper on a new CT machine, the invention would have to be found not inventive. At the same time, obviously, only few inventions can reasonably appear to be obvious to the man in the street in view of the daily paper, and it is unlikely (ie, implausible to assume) that anything can be obvious to that person in view of a paper on quantum computing. Hence, it is reasonable to assume the skilled person closer to the field of the application and/or the OTP. The person so chosen would be the most likely one to find the invention obvious and, conversely, if the invention were found to be non-obvious for that person, it might be reasonably assumed to be non-obvious for everybody else too. However, no other choice seems to be excluded as a matter of principle—under the crucial proviso that the person chosen has an ‘average’ skill and that it must always be made sure that the story as a whole does not go beyond what arguably would actually have happened.

Finally, it is noted that many decisions of the Boards of Appeal do not define the skilled person in any detail, which suggests that in many cases the ‘appropriate’ skilled person and ‘the art’ are not controversial.

The PSA is an attempt to make the inventive-step assessment ‘objective’ in that it should not depend on the ‘subjective’ or historical facts of the case to hand. In other words, the inventive-step assessment should not be made on the basis of how much—and which kind of—effort the real inventor had put into the invention or what problem the real inventor thought the invention would solve (the ‘subjective’ technical problem) but as much as possible on the basis of verifiable facts such as the available prior art. 66

The PSA assumes the skilled person to come up—or be confronted—with a technical problem (see also Section 5 below), the OTP, after having studied the CPA. According to the PSA, the OTP is derived from the comparison of the claimed invention and the CPA. It is this problem that is put to the skilled person or that the skilled person came up with.

Normally, the OTP should be one that the skilled person in the particular technical field would have been asked to solve at the priority date. Also, as formulated elsewhere, 67 the problem must be ‘meaningful for the skilled person, sufficiently concrete and specific’. If in doubt, this fact has to be established. 68 However, it may also happen that the problem itself appears to be non-obvious or one that the skilled person could not reasonably be assumed to have been faced with. In such a case, an inventive step might be acknowledged for the claimed invention as what is known as a ‘problem invention’, even if, knowing the (non-obvious) problem, the invention might appear obvious. 69

The OTP is ‘the aim and task of modifying or adapting the closest prior art to provide the technical effects that the invention provides over the closest prior art’. 70 ‘The’ technical effects in this regard must be demonstrated on the basis of the disclosure of the application as originally filed and the skilled person's knowledge as per the relevant (filing or priority) date. 71 It many cases it is evident for the skilled person that the distinguishing features have the alleged technical effects, in other cases it may be required that the application as originally filed disclose them or make them credible. A lesser degree of original disclosure may be sufficient if the effect is established by experimental data filed after the relevant date (‘plausibility’). 72

As already mentioned, the PSA has often been criticized as being based on hindsight, also because the OTP is derived from the comparison of the invention with the CPA. However, it must be stressed that specifically in order to avoid hindsight, the OTP is not formulated as ‘providing the distinguishing features’ but as ‘providing the technical effect(s) of the distinguishing features’. Irrespective of that issue, however, one might misconstrue this conventional formulation as implying that there is a unique OTP to be determined from the CPA and the claimed invention. Leaving aside the possibility that the claimed invention solves several independent, so-called ‘partial problems’, 73 this cannot be correct for a number of reasons.

First, the problem solved by the ‘technical effects of the difference’ can be formulated more narrowly or more widely. 74 The wider the problem is formulated, the less guidance would the skilled person have received from the problem formulation itself and the less obvious the solution might appear. For instance, the solution to a specific problem may not appear obvious from a problem formulated as ‘improving the prior art’ in an unspecified manner. At the same time, too general problems may be found unrealistic or at least to be insufficient motivation for the skilled person to become active at all; the solution might then be found to be obvious as an arbitrary choice from equally likely alternatives. It has been said that an essential idea of the PSA is to formulate the OTP based on the distinguishing features essentially as narrowly as possible 75 —without anticipating elements of the solution to avoid hindsight reasoning. 76

Second, it is possible that distinct effects can be ascribed to the same distinguishing features, and, accordingly, that different problems are solved by the claimed invention over the chosen prior art. In such a case, it will be necessary to consider several OTPs before an inventive step can be acknowledged. 77 Although this principle has not often been formulated in express terms, it has been acknowledged in the case law that, if an invention is found obvious as the solution of an OTP, additional and possible less obvious effects cannot overturn the finding of obviousness. Such effects are often referred to as (mere) ‘bonus’ effects. 78

Third, one might ask whether it is correct to derive the OTP from the effects of the distinguishing features in a way so that the claimed invention must be a (complete) solution to the OTP. It is conceivable that the claimed invention does not specify all (essential) features of the solution to some OTP so that the claimed invention contributes to solving the OTP but falls short of solving it entirely. In such a case, a solution of the OTP will at least fall within the scope of the claimed invention. By showing that this solution would have been obvious for the skilled person, it can be established that an embodiment of the invention, even if not specifically claimed, lacks an inventive step within the meaning of Article 56 EPC. 79 As a claimed invention must be inventive over substantially its whole scope, 80 it follows that the claimed invention as a whole lacks inventive step.

As mentioned before, the crucial consideration seems to be whether the OTP is one the skilled person can reasonably be assumed to have addressed in view of the CPA.

There has been a degree of controversy in the case law of the Boards of Appeal as to who defines the skilled person, the CPA and the OTP and in which order and who provides the OTP to the skilled person.

In some decisions of the Boards of Appeal, it has been assumed that the skilled person would, themselves, ‘select’ the CPA in view of the invention at hand. 81 This scenario is based on the narrative that a particular skilled person tries to solve a particular, given technical problem. In this scenario, the skilled person would be determined by the field defined in the application and the problem put forward by the applicant, that is, the ‘subjective’ technical problem. In a way, this tells the story on which the application itself is based. If it can be shown that this skilled person, setting out to solve the ‘subjective’ technical problem, would select a particular piece of prior art and, in so doing, be led to the invention in an obvious way, the claimed invention cannot be inventive within the meaning of Article 56 EPC.

This approach does not, however, comply with the fundamental idea of the PSA that the problem put to the skilled person is the ‘objective’ one derived by comparing the CPA with the claimed invention. When the OTP is derived from the CPA, it is logically impossible that the CPA is selected ‘in order to’ solve the OTP. In particular, it is impossible to conceive the skilled person to ‘select’ a CPA in an attempt to solve a problem that has yet to be defined. Also, the skilled person cannot ‘select’ the CPA in view of an invention which they do not know. At best, the deciding body, that is, the examining or opposition division or the Board of Appeal, might be considered to make such a ‘selection’ when, in deciding on inventive step, they give reasons why a document should be considered as CPA and therefore be the basis for a more detailed assessment of obviousness. 82

It has been found that the skilled person must be skilled in the art required to address—if not solve—the OTP. This narrative explains that the skilled person is determined by the OTP. 83 In one decision, it was vividly formulated that the skilled person ‘enters the stage only when the’ OTP ‘has been formulated in view of the selected’ CPA. 84 This is a consistent way of telling the PSA story—provided, in the author’s view, that it be made sure that the OTP is one that it was reasonable to assume the skilled person would have been asked to solve in view of the CPA.

Another way of looking at this is to say that the OTP does not ‘determine’ the skilled person but only allows one to exclude persons of certain skills because their efforts will predictably fail to arrive at the claimed invention. It is, however, quite a natural scenario to consider the skilled person to be the skilled addressee of the CPA and to ask whether the OTP would be one this person would have wanted or been asked to solve. 85 If that is the case, be it due to an explicit prompt in the CPA or in the skilled person’s general striving for improvement, and it turns out that, in doing so, they would have found the claimed invention obvious, a lack of inventive step within the meaning of Article 56 EPC would be established. If it is found that the skilled reader of the CPA would not have found the claimed invention obvious, however, this might not be the end of the story. A different skill than that needed merely to understand the CPA might be required to address and solve the OTP and a person with such a different skill might be shown to find the claimed invention obvious. Again, a lack of inventive step would ensue.

In summary, it is the author’s view that the PSA does not require the skilled person to be determined after the CPA and the OTP, but allows the skilled person to be determined independently of both.

A patentable invention is generally understood as one that solves a technical problem. 86 The EPC does not define what is technical but is taken to illustrate, namely in Article 52(2) EPC, what are examples of non-technical fields. Features that belong to any of these fields—which are, as such, excluded from patentability—are referred to as ‘non-technical’ features. Inventions comprising technical and non-technical features are called ‘mixed inventions’. Computer-implemented inventions (CII) are typically mixed in this sense, where a computer system, comprising at least some technical features, is used to implement a non-technical method, for instance, a business method. 87

Inventive step of mixed inventions, CII in particular, is typically assessed according to an adaptation of the PSA, which is often referred to as the COMVIK approach. 88 The COMVIK approach is defined to reflect the idea that patents are granted for technical inventions and that an inventive step can only be acknowledged on the basis of features, which, in the context of the claimed invention, make a technical contribution. 89

In one of the early decisions, which are said to further define the COMVIK approach, it was held that the ‘state of the art’ within the meaning of Article 54(2) EPC should be construed as comprising only information ‘relevant to some field of technology’ and that anything unrelated to any technological field or from which a skilled person would not expect to derive any technically relevant information does not belong to the state of the art to be considered in the context of Articles 54 and 56 EPC. 90 This finding was criticized in the literature, 91 and a more recent decision contradicted it. 92 The invention dealt with the automation of a signature procedure in a notary’s office, which was undocumented but accepted by the appellant to constitute common general knowledge. The deciding Board started its inventive-step assessment from just that procedure and considered that a ‘person skilled in the field of automation’ would have found the claimed solution to be an obvious way of automating a given and well-known method. Arguably, this starting point of the inventive-step assessment was a non-technical method 93 or at least one that did not anticipate any automation. The skilled person was, however, construed as one qualified in the art of automation rather than in the relevant law such as a notary. The scenario thus could be that of a computer scientist sitting in the notary’s office and wondering why it was necessary for that signature to come in person. 94

The author considers questionable the restriction of prior art according to what is ‘technical’. First, it cannot be determined a priori which documents are ‘relevant’ to some field of technology. For instance, to technologies that are crucially based on mathematics (for instance cryptography, pattern recognition or queuing theory), mathematical papers may evidently be relevant. More generally, in view of the development of technology, which patent law must be flexible enough to address, it cannot, in the author’s view, be defined a priori from which documents the skilled person would ‘expect to derive any technically relevant information’. And finally, any scenario in which someone, irrespective of that individual’s skill, can be assumed to scratch an itch 95 and sets out to solve—or have someone solve—a technical problem seems to be an equally valid plot for a convincing inventive-step story according to the PSA.

The COMVIK approach relies on the idea that features that do not contribute to the technical character of the invention cannot contribute to inventive step 96 and, based on this ratio, construes such features as part of the problem rather than the solution, which must be technical. Accordingly, it finds it to be consistent with the principle that the OTP shall not contain pointers to the solution, if such features appear in the formulation of the OTP. 97

While at first glance this appears to be a simple principle, the decision as to which features exactly can be discounted from the solution and be assumed to be given to the (technically) skilled person as a ‘framework of the technical problem that is to be solved’, a ‘constraint that has to be met’ or a ‘requirements specification’ 98 is not always straightforward. The case law of the Boards of Appeal has many examples for this. 99 As an aid for this decision, another animate actor in the inventive-step story has been proposed in the case law of the Boards of Appeal, referred to as the ‘notional business person’. This person is used as a reference for the decision of what requirements can ‘actually’ be given to the technically skilled person. 100 Although a character with less immediate support in the EPC than the skilled person, the notional business person seems to have acquired a fixed position in the PSA cast for computer-implemented inventions. 101 It has been anticipated that other persons of non-technical skill might join in the future. 102

A final point seems worth making. In a typical class of computer-implemented inventions, an implementation of a business method on some conventional computing hardware is claimed. According to the COMVIK approach, the business method will be assumed to be given the skilled person who is tasked with implementing it on the claimed computing hardware. In this scenario, the computing hardware is generally considered to constitute the CPA within the PSA, the OTP becoming ‘how to implement this business method on that platform’. If it is a generic computing platform commonly used to implement similar business methods, this OTP is a plausible automation request that the skilled person may be asked to carry out. 103 When the computing platform becomes more specific, however, it might, at some point, require express justification why the skilled person would have been asked to implement the given business method on just that computing platform or whether a potential inventive step could reside in the choice of that computing platform to implement the business method. 104

The author shares the opinion of many that the PSA is a very helpful tool for assessing inventive step. It provides a well-established and fairly predictable master story to be used for explaining whether a person having average skill in the art, in view of the state of the art, would or would not have arrived at a claimed invention.

A central advantage of this story is that each of its many details can come under separate scrutiny. Rather than discussing the rather complex and abstract requirement of Article 56 EPC in its entirety, it can be discussed separately whether a piece of prior art constitutes a suitable starting point, what precisely are the differences between that piece of prior art and the claimed invention, what (technical) effects these differences have, whether these effects interact with each other, who is a suitable skilled person and what are their skills, whether that skilled person, in view of the selected piece of prior art, would have addressed the problem of ‘achieving the technical effect(s) of the differences’ and, if so, what the skilled person would, rather than merely could, have done 105 (or considered doing 106 ) in order to solve the problem posed.

Once all these issues have separately been considered, there is a good chance that the resulting story about inventive step will be acceptable to the parties.

The author considers that these advantages of the PSA remain even when no general restrictions on the choice of the CPA, the OTP or the skilled person are imposed. It would appear that a claimed invention would have to be found to lack inventive step, if, for almost any skilled person (of at most ‘average’ skill), piece of prior art and technical problem, it could be shown that this person, in view of this prior art and setting out to solve this technical problem, would have arrived at the claimed invention in an obvious manner, provided that it could be justified that this particular person would have considered this particular prior art and addressed this particular technical problem so that the overall story remains a plausible one. Just as it is a matter of economy to select one piece of prior art as the CPA—or at least few of them—, so is selecting a technical problem the solution of which clearly yields the invention, and a person with the skill likely to succeed in solving the given problem. From this perspective, the criteria developed in the case law of the Boards of Appeal as how to define the skilled person, the CPA and the OTP are a matter of heuristics rather than strict requirements.

MM Fischer, ‘The Problem and Solution Approach – Basic Case Law and Recent Development (I)’, epi information 3/2016.

See, for instance, the EPO Guidelines for Examination, G-VII, 5: ‘In order to assess inventive step in an objective and predictable manner, the so-called “problem-solution approach” is applied’; and R5/13, point 15, ‘… the problem-solution approach is the key element for the assessment of inventive step and is the one which is applied first and foremost’.

Or ‘stock story’; see S Paskey, ‘The Law is Made of Stories: Erasing the False Dichotomy between Stories and Legal Rules’ Legal Studies Research Paper Series, Paper No. 2015–003, SUNY at Buffalo Law School. Published in Legal Comm. & Rhetoric, JALWY, vol. 11, Fall 2014 and on the Social Science Research Network (SSRN) Electronic Paper Collection, Available at https://ssrn.com/abstract=2507485 ; D Rees, ‘Inventive Step: The Stories We Tell’ (2017) Available at https://ssrn.com/abstract=2952332 (accessed 10 November 2021).

T24/81, headnote; GSA Szabo, ‘The Problem and Solution Approach to Inventive Step’ 10 (1986) EIPR 293–303. Szabo was an early member of the Boards of Appeal of the EPO who was intimately involved in the development and presentation of the problem-solution approach. As will be seen, his early papers contain quite a few statements on the matter, which are still worth reconsidering.

As once formulated by an anonymous commentator on a case law blog a; see D Pearce, ‘Problem-Solution Approach: ur doin it wrong’, 17 February 2010, IPKat, Available at https://ipkitten.blogspot.com/2010/02/problem-solution-approach-ur-doin-it.html (accessed 10 November 2021).

Although the considerations presented in this paper are meant to be widely, if not generally, applicable, it may be worth stressing that the author’s considerations are based on experience primarily in the field of computing technology.

Equivalent to Rule 27(1)(c) EPC 1973.

See Rees, supra, at 3.

See GSA Szabo, ‘The Problem and Solution Approach in the European Patent Office’ 26 (1995) IIC 457; ‘… demonstrate the lack of the inventive step by some reproducible mental procedure, and recognise inventiveness whenever the suggested formalised approach does not work’.

For the general idea, see Paskey, supra, at 3, 52: ‘… the elements of the rule correspond to the elements of a story and have a logical relationship that qualifies as a “plot.” Second, the analytical moves we think of as rule-based reasoning are often a form of narrative reasoning, in which the story in a given set of facts is compared to the stock story embedded in the rule. […] lawyers do not rely on stories simply because they are persuasive. They do so because every governing rule demands a story: a story is embedded in the rule’s structure, and the rule can be satisfied only by telling a story’.

At least as identified by the EPC; see Sections 4 and 6 below.

And even that, strictly speaking, only for the invention as described in the application as originally filed (Rule 42 EPC), ie, before the search report has been drawn up. See also M Müller, ‘The Patentable Invention’ in F Macrez and T Debled (eds) Quel degr é   d’harmonisation du droit des brevets en Europe? — Jurisprudence France — OEB: convergences et divergences (LexisNexis, coll. CEIPI, 2020) (forthcoming).

See Paskey, supra at 3, 52, 59 and 63; Paskey states on page 59 that ‘legal rules inherently possess three key traits: (1) the rules refer to people, things, events, and circumstances; (2) those references are stated in general terms; and (3) the elements of the rule necessarily have a logical coherence’.

GL G-VII, 5; Case Law of the Boards of Appeal of the European Patent Office, 9th edition, July 2019, (henceforth CL) I.D.2; see also T24/81, headnote I, which states that ‘objectivity in the assessment of inventive step is achieved by starting out from the objectively ruling state of the art, in the light of which the technical problem is determined which the invention addresses and solves from an objective point of view, and consideration is given to the question of the obviousness of the disclosed solution to this problem as seen by the man skilled in the art and having those capabilities which can be objectively expected of him’ (or her, for that matter).

It will become clear below why the author prefers putting the term ‘closest prior art’ in quotes.

GL, G-VII, 5.1; Case Law of the Boards of Appeal, I.D.3.

Even ‘a Mickey Mouse journal’ is possible, see Szabo, supra at 9.

GL, G-VII, 5.2 and 5.4; CL, I.D.4.

Several presentations of the PSA are available at different degrees of detail. See, eg, P de Lange, ‘The modern problem-solution approach’, epi information 2/21; D Closa et al.   Patent Law for Computer Scientists (Springer Verlag, 2010), 27; and J-M Deltorn, ‘Du Vibranium à l’Adamantium: la mesure de l’activité inventive et l’approche problème-solution’, Manuel CEIPI—Proprieté intellectuelle et pop culture, 2021.

M Wilming, formulated this idea as ‘Even though case law should be predictable, individual judgments must be “right”’ in a contribution to the blog patentlitigation.ch entitled ‘My constant struggles with how the problem-solution approach is applied (or not)’, 20 April 2021.

T465/92 Aluminium alloys, headnote.

To the best of the author’s knowledge.

See Szabo, supra at 9, and F Hagel et al. , ‘Making proper use of the problem-solution approach’, epi information 1/1995. See also Rees, supra at 3, who explains that enquiring what could or would have happened under certain conditions but did not actually happen, asks for the truth condition of a ‘counterfactual’ conditional statement, which to determine is notoriously difficult, to say the least.

Inventions are made in very different ways, which are difficult to establish and compare and which do not provide a reliable basis for assessing the actual contribution of the invention. The act of inventing may take place unpredictably and in unlikely places, think of the story claiming that Archimedes suddenly understood buoyancy—and conceived a way of determining whether a crown was made of pure gold or of inferior material—while taking a bath or the one according to which Sir Alexander Fleming accidentally detected the antibiotic effect of penicillin after having failed to clean his lab material. Other—maybe most—inventions require more active work as the famous inventor Thomas Alva Edison is said to have suggested by saying that genius—and invention—is made up mostly of transpiration and only little of inspiration. See also J Pagenberg, ‘The Concept of the “Inventive Step” in the European Patent Convention’ (vol 9/10., eg 39 1974) IIC 157, section II.

Such as the requirement that one citation must be selected as being closer than others, which may or may not be considered to belong to the ‘essence’ of the PSA; see T465/92, r. 9.3, and Section 2 below.

Rees, supra at 3, also considered alternative master stories.

See also Szabo, supra at 4, 293: ‘Instead of taking an arbitrary starting point for the invention, as a modification of what was already specifically known, it is more reasonable and economic to select the “closest prior art” for the purpose’. Notably, also Szabo puts the term ‘closest prior art’ in quotes, apparently implying that it is primarily a convenient label. See also T570/91.

See T320/15.

See, eg, T606/89.

See, eg, T644/97, T334/10 Enovin/JANSSEN PHARMACEUTICA and T1087/15.

See, eg, A Scheuchzer, Nouveaut é   et activit é   inventive en droit europ é en des brevets (Librairie Doz, Genève, 1981) 404: ‘L’inventeur, face au problème qu’il cherche à résoudre, ne se dit pas: ‘Je vais transposer quelque chose, mais je n’ai pas encore trouvé quoi’. La transposition, en tant qu’opération de la pensée, n’existe pas indépendamment de l’objet auquel elle s’applique’. In a way, looking for a new use of a known technology would qualify for a solution-problem approach rather than vice versa . The author does not wish to exclude that this way of presenting an inventive-step objection may be convincing in particular circumstances. For instance, where a class of mathematical algorithms is known to be applicable for several different applications, the invention concerns the use of such an algorithm for one application but a prior art document discloses it specifically only for another one. In order not to digress further, reference is made to the pertinent discussion in T1019/99, r. 5, and T 2360/08, r.1 and 2.

See, eg, T254/86 and T656/90. Notably, the choice of ‘promising’ in this context is not meant to imply that the finding a lack of inventive step is preferable over finding an inventive step; see a comment by F Hagel on a case law blog (K Füchsle and T Bausch, ‘The Problem of the “Closest Prior Art”’, Kluwer Patent Blog, 24 June 2020, Available at https://patentblog.kluweriplaw.com/2020/06/24/the-problem-of-the-closest-prior-art (accessed 10 November 2021).

O Randl, ‘T56/09—So Close’, blog post on K’s law, Available at https://k-slaw.blogspot.com/2012/09/t-5609-so-close.html (accessed 10 November 2021).

See, eg, T967/97 Chipkarte/OVD KINEGRAM AG, headnote I, and T21/08.

And even irrespective of whether the prior art can be considered ‘non-technical’ (see Section 6 below), T2101/12 Authentication binding document with signature/VASCO. Interestingly, this already appears in Szabo’s 1986 paper on the PSA, supra at 4, 293: ‘It goes without saying that the invention must be non-obvious vis-à-vis anything and everything known in the art, and a problem could therefore arise in relation to any disclosure in this respect’. See also T405/14 Self-testing sensor/WILLIAM L. SMITH, r. 19; T694/15 Visualisation/COUNTERFLO, r. 13–14; T1112/19 Replay of data/GOLDMAN SACHS, r. 2.1.3; and others.

See, T967/97 Chipkarte/OVD KINEGRAM AG, headnote II.

See T1742/12 On demand instantiation/RAYTHEON, r. 10.3.

See T1742/12 On demand instantiation/RAYTHEON, r. 9; similarly T2304/16, r. 4.2.5 and T2443/18, r. 2.8.

AW White, ‘The Problem and Solution Approach to Obviousness’ (vol 12., 1986) EIPR 387. R Jehan, ‘The Problem and Solution Test in the Assessment of Inventive Step’, epi information 2/1995; GSA Szabo, ‘Clarifying addendum to the problem-solution approach’, epi information 1/1995.

See Article 92 EPC.

Dr Watson to Sherlock Holmes: ‘Anything seems commonplace, once explained’ (Arthur Conan Coyle).

See in this regard also R3/10, r. 2.10, and R10/13, esp. r. 16.

See Szabo, supra at 9: ‘Actually, if the “closest”, i.e. the most dangerous, starting point does not lead to a conclusion of obviousness, there would hardly be a good reason to assume that the other starting points might do better. Nevertheless, if an opponent still relied in such a situation on some other documents as his preferred “closest” art, this would also have to be assessed in the decision to show convincingly that the alternative route is equally unsuccessful’.

See T855/15 Security architecture/WONDERWARE, r. 8.2, and, agreeing, T1450/16 Acoustic port of a hearing device/SHURE, r. 2.1.4, last sentence; see also Szabo, supra at 9: ‘[…] single starting point […] This source is not considered to have been found by the skilled person searching in view of a preconceived purpose, e.g. a problem to be solved, since […] It must be assumed that the primary source could have accidentally become available to a skilled person anywhere in the world […] by chance. This could be taken as the second maxim of the “approach”’.

Also known as ‘the man on the Clapham omnibus’, first referred to in McQuire v Western Morning News Co Ltd [1903] 2 KB 100, or, in Australia, ‘on the bondi tram’, introduced in Papatonakis v Australian Telecommunications Commission [1985] HCA 3; 156 CLR 7.

EuGH, Rs C-210/96 Gut Springenheide GmbH and Tusky v Oberkreisdirektor des Kreises Steinfurt; or the ‘moron in a hurry’, coined by Justice Foster in Morning Star Co-Operative Society Ltd v. Express Newspapers Ltd Morning Star [1979] F.S.R. 113.

See, eg, T301/09 and R17/09.

See, eg, L Zwiffelhoffer, ‘Die Figur des Durchschnittsmenschen im Verwaltungsrecht’ Mohr Siebeck, Beiträge zum Verwaltungsrecht, 2020, and examples therein.

See T60/89.

See T1462/14, r.14.

See, eg, Case Law of the Boards of Appeal, I-D, 8.1; and, for the similar concept of the ‘person having ordinary skill in the art’ in US patent law, see eg NJ Gulati, ‘Knowledge/Skill Standards of a “Person Skilled in Art”: A Concern Less Visited’ (2018) 17 J. Marshall Rev. Intell. Prop. Law 588.

See, eg, T39/93 Polymer powders, headnote 3; T207/94; T1396/09.

See T391/91.

But never bored; see, eg, Gulati, supra at 51.

See [2004] RPC 919, Rockwater Ltd v. Technip France SA.

See T500/91.

See T1157/06, T632/10 Re-signing electronic documents/SAP, r. 6.2, and further references therein.

See, eg, T141/87, r. 3.6, T99/89, r. 4.3, T783/94, r.3.3, T402/95, r.3.3, and T986/96, r. 3.1.1.

See T57/86, r. 5.6; T15/15, r. 4.4; [2010] EWCA Civ 819, Schlumberger Holdings Ltd v. Electromagnetic Geo Services AS.

See T190/99, catchword.

See, eg, J-L Comte, ‘L’ homme du métier en droit des brevets’, sic! Zeitschrift für Immaterialgüter-, Informations- und Wettbewerbsrecht, 7/2000.

If necessary and plausible, the skilled person may also be construed as a team which, together, provides the relevant set of skills; see, eg, T15/15, r. 4.4.

See, eg, T60/89.

See T422/93, headnotes 1 and 2, and T1450/16 Acoustic port of a hearing device/SHURE, r. 2.1.4.

See T2101/12 Authentication binding document with signature/VASCO.

See Szabo, supra at 4, 294: ‘It follows that the way the invention was made is irrelevant. This can be contrasted with a subjective or historical approach which tries to assess the invention by considering the inventor’s own progress from certain disclosures incidentally available to him’.

F Hagel et al. ‘Making proper use of the problem-solution approach’, epi information 1/1995.

See T641/00 Two identities/COMVIK, r. 5; see also T905/09 Antropomorphized toy/EIGHTING, r. 9; T643/10, r. 9, and others.

Notably, the term ‘problem invention’ is a misnomer, as the invention is not constituted by the problem but merely non-obvious in view of it. See Szabo, supra at 4; A Kennington, ‘A Review of the “Problem and Solution” Approach to Inventive Step under Article 56 EPC – Part 1 – The Correct Formulation of the Problem’, epi information 1/2016; F Hagel et al. , ‘Making proper use of the problem-solution approach’, epi information 1/1995. See also, eg, T11/81, r. 3.

See the GL, G-VII, 5.2.

See, eg, T1958/13 Single-drag gesture/LG, r. 2.2.5 and CL, I-D, 9.1.5; see also MM Fischer, ‘The Problem and Solution Approach – Basic Case Law and Recent Development (II)’, epi information 4/2016.

What this degree should be, in view of the rationale that the application is originally filed must establish that the invention was actually made at the relevant date, is an aspect of a pending referral to the Enlarged Board of Appeal, see T116/18 Insecticide compositions and G2/21.

See, eg, CL, I-D, 9.2.2.

See, eg, W17/03 Radio frequency identification/3 M, catchword 3.

See W17/03 Radio frequency identification/3 M, catchword 2.

See again the GL, G-VII, 5.2, but also T229/85 Etching process, headnote.

See T694/14 Visualisation/COUNTERFLO, r. 15; see also Szabo, supra at 9: ‘The skilled person has a natural right to follow up on any one of the problems recognised. It is immediately clear that most of them would never lead to the invention, since the latter does not provide the required effect. Only those where the follow up of a problem might point towards the invention are worthwhile to consider’. In order to find obviousness, consideration of one OTP may suffice, see T2348/16, r. 18.

See, eg, the GL, G-VII, 10.2.

A way of looking at this is that the PSA has been correctly applied to an embodiment of the claimed invention, which was not expressly claimed itself.

See, eg, T939/92 Triazoles, headnote 2, and G1/19 Pedestrian simulation, r. 82.

See, eg, the references in T1450/16 Acoustic port of a hearing device/SHURE, r. 2.1.4.

See T855/15 Security architecture/WONDERWARE, r. 8.2; in agreement T1450/16 Acoustic port of a hearing device/SHURE, r. 2.1.4; in only partial agreement T2057/12, r. 3.2.2.

See T32/81, T141/87, r. 3.5, and T422/93, headnote 1.

See T1450/16 Acoustic port of a hearing device/SHURE, catchword.

For instance, one might say that a person skilled in the art of washing machines or household appliance would not be minded to solve a problem in car manufacturing, and that it is unrealistic to assume a person skilled in both fields. For further examples see, eg, T800/91, Heat-shrinkable film/KUREHA, r. 6; T1213/15 External interface/JOHNSON&JOHNSON, r. 10.2.2; T1601/15, r. 3.5.

See, eg, HG Hesse, Die Aufgabe — Begriff und Bedeutung im Patentrecht (GRUR 1981, 853), section IV.1; see also Rule 42(1)(c) EPC.

See M Müller, supra at 12, and W Chandler, ‘Patentability of computer-implemented inventions (CIIs): state of play and developments’ OJ EPO, Supplementary publication 5/2015, pp. 73–79.

See, in particular, T641/00 Two identities/COMVIK; T154/04 Estimating sales activity/DUNS LICENSING ASSOCIATES; G3/08 Programs for computers.

See T641/00 Two identities/COMVIK, headnote 1, and G1/19 Pedestrian simulation, r. 33.

See T172/03 Order management/RICOH, headnotes 1 and 2.

See in particular S Sterckx and J Cockbain Exclusion from Patentability – How Far has the European Patent Office Erodd Boundaries? (Cambridge University Press, 2012) 86.

T2101/12 Authentication binding document with signature/VASCO.

Even though, strictly speaking, any implied handling of paper would, according to T258/03 Auction method/Hitachi, r.4.6, make the method a ‘technical’ one.

A type of question which was addressed and solved aplenty to enable homeworking during recent times of Covid-19.

See also lesson 1 in ES Raymond, ‘The Cathedral & The Bazaar – Musings on Linux and Open Source By an Accidental Revolutionary’, O’Reilly Media, 1999: ‘Every good work of software starts by scratching a developer’s personal itch’.

See, eg, T1453/17, r. 2.2.

See T641/00 Two identities/COMVIK, headnotes I and II.

See T641/00 Two identities/COMVIK, headnote II, and T172/03 Order management/RICOH, r. 16.

For a possible entry into this issue, see, eg, T1670/07 Shopping with mobile device/NOKIA; T1741/08 GUI layout/SAP; T1755/10 Software structure/TRILOGY.

See T1463/11 Universal merchant platform/CardinalCommerce, eg, r. 13.

J Leeming, ‘The Notional Business Person – A New Actor on the IP Stage?’ J. A. Kemp Topical briefing, 3 May 2017, Available at www.jakemp.com ; MM Fischer, ‘Who is the notional business person?’ epi information 2/2020.

See T1463/11 Universal merchant platform/CardinalCommerce, eg, r. 13: ‘the business person (for example)’; T630/11 Gaming Server/Waterleaf, r. 9; T817/16 Document scoring/GOOGLE, r. 3.11 and 3.12.

Incidentally, one would probably arrive at the same result if one were to formulate the OTP merely as ‘implement this business method’ and leave it to a person skilled in the art of automation to think of choosing a common computing platform as an obvious choice to solve the problem.

See T1325/17 Location-based dating/LOCATOR, r. 10.2.

For the could/would approach, see T2/83 Simethicone Tablet, headnote 2, but also JB Van Benthem and NWP Wallace, ‘Zur Beurteilung des Erfordernisses der erfinderischen Tätigkeit (Erfindungshöhe) im europäischen Patenterteilungsverfahren’ (vol 6., 1978) GRUR Int. 219. It has always struck the author as trivial that inventive step cannot in general turn on what the skilled person ‘could’ have done because many patent applications in themselves are proof that at least someone of appropriate average skill was able, as a matter of fact, to come up with the invention by combining individually known features. Even more so is the obligation to focus on what the skilled person ‘would’ have done one of the most important safeguards against hindsight reasoning.

It has been suggested that the could/would approach would not apply in certain situations, such as when the OTP was formulated as “finding an alternative solution” (see, eg, T1968/08, r. 5.5) or where the invention amounted to an arbitrary selection from many possibilities (see, eg, T12/07 Aggregation of proteins/QUADRANT DRUG DELIVERY LIMITED, r. 4.1.6), especially “equally likely” or “equally obvious” alternatives (see, eg, T1045/12, r. 4.7.7, or T894/19 Rotatable snapping connection/OTICON, keyword, r. 3.6). However, finding one of several options to be obvious as an “arbitrary” selection of “equally likely” or “obvious” alternatives still requires at least the judgment that the skilled person would have recognized as equally likely or obvious, and thus considered, all the alternatives to pick from when trying to solve the OTP. Beyond that, no specific pointer to any one of the alternatives may be required. In the author’s view, however, this does not mean that the could/would approach does not apply.

Author notes

This presentation reflects the author’s personal opinion. The author would like to thank Iulian Alecu, Frédéric Bostedt, Miguel Domingo Vecchioni and Richard Winkelhofer for helpful remarks. All remaining errors and inaccuracies, however, remain the author’s responsibility alone. The author owes this perspective to a large degree to his former colleague and friend Dai Rees, himself at the time chairman of Technical Board of Appeal 3.5.06, and his inspirational article on story-telling in patent examination (see footnote below, infra 3). On 21 December 2021, Dai Rees left us too soon. This article is dedicated to Dai.

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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The problem-solution approach in determining inventive step

• Kathy Wasström

Inventive step is one of the most important criteria of a patentable invention. At the same time it is one of the most difficult criteria to define.

In order to be inventive, an invention should not be obvious to a person skilled in the art. The term “obvious” is, in turn, typically defined by evaluating whether a particular development is to be seen as a part of the expected progress of the relevant technology, or whether it could be considered unexpected.

A few different methods have been developed to help with the evaluation of inventive step. The problem-solution approach is a commonly used method particularly in Europe.

Although the original goals of said approach included that it would make it possible to evaluate inventive step in an objective manner, by avoiding hindsight, particularly the latter part of this goal has been challenging, also using this method. A successful evaluation of inventive step does require the evaluation of the claim features as if these features would not be known.

However, the problem-solution approach is still highly useful.

Based on the Guidelines for Examination, originally drawn up for the Examiners of the European patent office, the problem-solution approach contains three main steps:

• selecting the closest prior art among the available publications,
• defining the objective technical problem, and
• evaluating the invention based on these.

1. Closest prior art

The closest prior art is the publication that would have been the most promising starting point for any such development that would have resulted in the invention to be evaluated.

The most important issue to consider, when selecting the closest prior art, is that the publication should belong to the same, or a very close, technical field as the invention that is evaluated.

They can both, for example, describe a fibrous product, even if they describe products having different properties. Thus, the technical field could be “fibrous products”.

Secondly, the document representing the closest prior art should be intended for the same purpose as the invention to be evaluated, for example by aiming at improving the same property .

In practice, it is common to merely carry out a comparison of the structural and functional features of the invention and the corresponding features described in the publication.

2. The objective technical problem

In defining the objective technical problem, the differences between the invention to be evaluated and the document selected in the previous step to represent the closest prior art are first determined, as well as the effects or advantages achieved using these differences.

Typically, the definition is based on asking how a specific effect or advantage, that is not achieved using the closest prior art, could be achieved for a specific method or product in a specific technical field.

The objective technical problem can be said to be a problem that is solved by the invention to be evaluated, but not solved by the closest prior art. It may for example be related to an improvement of the solution of the closest prior art, or it may relate to an alternative manner of achieving a certain desired effect, i.e. a manner that is different from the one of the closest prior art.

This is a difficult step of the method, where also a patent professional may fumble. It is very easy to take a shortcut in defining the objective technical problem, and merely make a general comparison of the improvements made in the new invention to various known alternatives, or combinations of such known alternatives. This does, however, not comply with the guidelines for the problem-solution approach.

In defining the objective technical problem, only the document selected to represent the closest prior art should be used for said comparison. No other known alternatives should be taken into account in this step, no matter how well known they are.

3. Final evaluation of the invention, i.e. does the prior art, overall, guide the person skilled in the art in the right direction?

In the final step of the problem-solution approach, it should be determined whether the person skilled in the art could solve the objective technical problem defined in the previous step, using one further disclosure.

In other words, would the person skilled in the art, based on a second disclosure, have made the decision to carry out the needed changes or improvements to the disclosure of the closest prior art in order to achieve the invention to be evaluated.

Therefore, other prior art, in addition to the closest prior art, can finally be considered in this step of the problem-solution approach. More precisely, the disclosure of the closest prior art can now be combined with the teachings of one other publication.

For example, a method to be evaluated might be considered obvious (not inventive) if it can be achieved by adding one method step from a second publication to the method of the closest prior art.

Such a combination of teachings from two prior art documents is acceptable if it can be demonstrated that the person skilled in the art would have had a reason to read the second disclosure. This second document being from a similar technical field as the closest prior art is, however, a perfectly acceptable reason.

The combination of teachings should also be simple to perform, and not require any unreasonable modifications of the steps already disclosed in the closest prior art. Preferably, the closest prior art should also contain some incentive that guides the person skilled in the art to find improvements in the type of technology that is described in the other document.

If such an acceptable combination of documents is found, the invention to be evaluated is considered to be obvious.

Recent developments

In the past, it has been possible, for example when responding to an Office Action, or in opposition cases, to argue in favor of, or against, inventive step by briefly referring to the differences between the invention and the closest prior art, and to the advantages achieved using these differences, or the lack thereof.

However, during the past years, patent offices have adopted a more strict approach, where the complete problem-solution approach should be presented also in simple cases.

Even if it might feel unreasonable, it may have a clear advantage in some cases. When the complete problem-solution approach has been presented once, it can easily be referred to in subsequent proceedings.

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Problem-solution approach: Exercises

Course: problem-solution approach: exercises | e-learning centre.

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General aspects

In the following you can find an e-learning module that helps you to refresh your knowledge about the PSA.

Exercises: Chemistry

Exercises: Non-chemical fields

Case-law of the Swiss Federal Patent Court

My constant struggles with how the problem-solution approach is applied (or not)

Case No. O2018_004 | Decision of 14 December 2021

There is so much to write about this judgment that I hardly know where to begin. You might want to catch a glimpse of what is at stake on this Blog here . In my opinion, it is a judgment that would have deserved a headnote, maybe even more than one. A thorough discussion of all aspects will take some time. This is why I chose to take baby steps, to at least get things going. In this post, I will only address a tiny bit of the judgment concering the assessment of inventive step / problem-solution approach. A separate post will cover the other aspects of the decision, hopefully soon.

It hardly ever happens that I disagree with the assessment of inventive step in judgments of the FPC — as far as the result is concerned. But the reasoning sometimes puzzles me.

Case law should be predictable. Towards this end, it is comfy to have standardized tools at hand. This is where the EPO ’s problem-solution approach comes into play ( Guidelines, G-VII, 5 ) which the FPC has repeatedly indicated to apply. O2018_004 is no exception to the rule:

As a quick recap, the problem-solution approach involves three main steps:

• determining the ‘ closest prior art ‘;
• establishing the ‘ objective technical problem ‘ to be solved; and
• considering whether the claimed invention would have been obvious to the skilled person.

Even though case law should be predictable, individual judgments must be ‘right’. Accordingly, the judgment holds that the problem-solution approach shall not be formalistically but critically applied, to avoid hindsight bias, in particular in the formulation of the objective problem. I do concur (it’s even in the Guidelines, G-VII, 5.2 , third but last paragraph).

The judgment goes on to explain why:

Losely translated to English:

If the effects or problems associated with the distinguishing features cannot be inferred from the closest prior art and are not obvious for the skilled person in light of the teaching of the closest prior art, the schematic application of the problem-solution approach can and usually will result in the identified ‘objective technical problem’ already giving an indication of problems or improvements in a certain direction which cannot be inferred from the closest prior art and which is remote therefrom. 45

45 T 5/81 of 4 March 1982, OJ 1982, 249, ¶11; T 63/97 of 1 December 1997, ¶3.5; T 170/97 of 23 February 1998, ¶2.3; T 414/98 of 30 November 1999, ¶6.1.

That’s a looong sentence that I had to rehash several times to swallow it — and I am not sure if I’m done yet.

The decision goes on to hold:

In such situations, the objective technical problem must not be formulated in terms of the specific effects associated with the differentiating features; otherwise it would already give the skilled person a retrospective indication to even consider changes in a certain direction for improvements.

Well, … I disagree. It is perfectly fine in the problem-solution approach to include effects (Effekte) or problems (Problemstellungen) into the definition of the objective technical problem which are not disclosed or rendered obvious by the closest prior art. If that was not a given anymore, one would push the door gaping wide open for the test to deliver obviously wrong results.

Here is an example:

Let’s take a prior art document D1 that discloses a snow plow for mounting on a truck. The whole document is about the clever geometry of the plow itself. The mounting for connecting the plow to the truck is only shown schematically, not described in any detail. No discussion whatsoever about the mounting, or that there could be any issues with the mounting. Taken to the extreme: Let’s assume that D1 boldly holds that any mounting will be equally fine.

The later invention builds on the plow of D1, and improves the mounting. Let’s say, the inventive mounting for the plow is more strain resistant than any other mounting that had been known for snow plows of any kind. Let’s assume that this is due to rivetting instead of welding.

There is nothing wrong about a formulation of the objective technical problem to make the mounting of the plow according to D1 more strain resistant: If there is a secondary document or other teaching that fairly suggests a strain resistant mounting for a plow of the kind of D1, the invention is dead on arrival (rightly so). If not, an inventive step is to be acknowledged.

I would only see it differently in the rare case of the discovery of a previously unrecognised problem, so-called problem inventions . In the above example, let’s assume that previously known snow plow mountings rapidly broke and noone had ever understood why. If the issue of strain in comparable mountings had never ever been mentioned in the prior art, the formalistic appplication of the problem-solution approach would indeed lead to ‘wrong’ results. But, frankly, arguing for a problem invention typically is a desperate last resort, evidenced be a whole body of Case Law of the Boards of Appeal . What is more, posing of a new problem must be shown over the prior art as a whole (similar to a technical prejudice ), not only vis-à-vis the closest prior art. And the burden is on the applicant / patentee to do so, not on the office or court to come up with it.

If it would happen once in a while that the problem-solution approach cannot / must not be applied as we all know it, then I would expect that this would be mentioned in the EPO Guidelines . But there is … nothing.

Next, the references to case-law of the Boards of Appeal in fn 45 (see above) made me worry whether I missed anything.

Let’s see:

T 5/81 of 4 March 1982 (OJ 1982, 249) is so old, it’s almost prehistoric. The decision even predates T 24/81 of 13 October 1982 which has outlined the problem-solution approach for the very first time. The reasoning in ¶11 of T 5/81 evolves around a comparison of the problem indicated in the closest prior art document and the problem defined in the application as filed. That had been one of many approaches at the time to tackle obviousness. But not so anymore today. T 24/81 in no way sets itself apart from the problem-solution approach.  

As to T 63/97 of 1 December 1997, I feel that the reference to ¶3.5 is besides the point. The definition of the problem (step ii., above ) is already done in ¶3.4; ¶3.5 deals with the assessment of obviousness of the solution (step iii., above ). I have a vague fealing that the reference is meant to point to ¶3.5.3, holding the following:

An interpretation of the documents as influenced by the problem solved by the invention while the problen was neither mentioned or even suggested must be avoided, such an approach being merely the result of an a posteriori analysis (see decision T 5/81 , OJ EPO 1982, 249)

I do concur: Prior art documents must not be interpreted with hindsight. But this concerns the assessment of whether or not the solution had been obvious (step iii., above ), not the definition of the objective technical problem (step ii., above ).

Reference to T 170/97 of 23 February 1998 does not add much, at least at first glance. The objective technical problem is merely stated without any further ado in ¶2.3. What is interesting, though, is the reference to T 13/84 , which is the decision that had introduced the concept of re-formulation of the problem in view of newly cited prior art. In T 13/84 , the applicant argued that the preamble of the claim (reflecting the closest prior art) should relate to the same or a similar problem. The Board explicitly disagreed:

I have discussed a very similar issue on this Blog here in relation to the choice of the closest prior art, i.e. when it had been held in O2015_008 that the objective technical problem that is used for the problem-solution approach shall have a «basis or motivation in the closest prior art» document. I feel that T 13/84 supports my view that this is not correct.

T 414/98 of 30 November 1999 is besides the point, again. Reference to ¶6.1 concerns the assessment of obviousness of the solution in the problem-solution approach, i.e. step iii.,   above .  The definition of the objective technical problem is being dealt with in ¶5, in no special way.

In sum, none of the references in fn 45 supports the view that there is a systematic issue with the problem-solution approach when «effects or problems associated with the distinguishing features cannot be inferred from the closest prior art.» If that was indeed an issue, it would almost certainly have been dealt with in quite a number of decision of the Boards of Appeal meanwhile: There are thousands of decisions that have applied the problem-solution approch, over a timeframe of four decades. But it appears that there is not a single precedent.

Now that you followed me through this lenghty exercise to establish a line of reasoning why this approach is mistaken, you might wonder:

Does it make a difference?

Not in the present case, I believe. The secondary reference is technologically so remote from the closest prior art that one could well have denied obviousness in step iii. of the standard problem-solution approach.

But that does not mean it is irrelevant. It significantly impairs predictability of case-law, without any apparent need.

What is more, it might well make a difference in another case, which it shouldn’t. The problem-solution approach is an extremely valuable tool to ensure predictability of case-law since about 40 years in thousands of Boards of Appeal decisions, and tens of thousands of decisions to grant or refuse patent applications at the EPO on (non-)obviousness — each year.

The problem-solution approach surely is not the one and only tool to assess obviousness. But since the FPC opted to apply it as a rule, I would hope that it is only modified with a trembling hand if there really is a need for it. Apart from problem inventions, I cannot see any.

Reported by Martin WILMING

BIBLIOGRAPHY

Panel of Judges:

• Dr. Andri HESS
• Dr. Tobias BREMI
• Lara DORIGO

Judge-rapporteur:

Court Clerk:

• Susanne ANDERHALDEN

Representative(s) of Plaintiff:

• Dr. Michael RITSCHER (MLL)
• Louisa GALBRAITH (MLL)
• Werner ROSHARDT ( Keller Schneider ) , assisting in patent matters
• Stephan KESSLER ( Keller Schneider ), assisting in patent matters

Representative(s) of Defendant:

• Dr. Ralph SCHLOSSER
• Dr. Regula RÜEDI ( Blum ), assisting in patent matters
• Dr. Christoph ENGELBRECHT ( Blum ), assisting in patent matters
• Dr. Zacharias STELZER ( Blum ), assisting in patent matters

DECISION IN FULL

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Navigating the EPO’s “problem-solution approach”—Part I

No matter where in the world you would like to file a patent application, the key patentability requirements in all jurisdictions are essentially the same: novelty and inventive step (in some places also referred to as non-obviousness). According to these requirements, the invention must not be identical to something that is already available to the public (novelty) and the invention must not be a mere trivial modification of the prior art (inventive step).

The European Patent Convention (EPC), which provides the legal basis for granting European patents by the European Patent Office (EPO), states that an invention shall be considered as involving an inventive step, if having regard to the state of the art, it is not obvious to a person skilled in the art (Article 56 EPC). At first sight, one might justifiably think that therefore the only relevant question for assessing an inventive step is whether the invention is obvious to the skilled person having regard to the state of the art. This is however not what the EPO does for assessing inventive step. Since its inception in 1977, the EPO has established a rather unique approach to assess the presence of an inventive step, by breaking up the one question of obviousness, which is explicitly stated in the law, into three separate questions.

a) What is the closest prior art?

b) Which technical problem does the invention objectively solve vis-à-vis the closest prior art?

c) Would it have been obvious to the skilled person at the relevant date to solve this objective   technical problem in a way that falls within the terms of the claims?

This approach is generally called the “problem-solution approach” ( EPO Guidelines for Examination, G-VII.5 ). It is often argued that the roots of the “problem-solution approach” can be traced to Rule 42(1)(c) EPC, according to which the description of the European patent application shall disclose the invention in terms of a technical problem and an offered solution to the problem.

Leaving aside the question of where this approach has its statutory footing, it is important to note that the Boards of Appeal of the EPO over the years have developed this approach in an attempt to provide an objective way for assessing inventive step, avoiding hindsight when considering the prior art. The EPO’s approach tries, what otherwise might be difficult to accomplish, namely to force the person making the assessment into the shoes of the notional skilled person at the relevant date—as it were, when the invention did not yet exist, and from this perspective ask the question whether the invention is obvious over the prior art. Of course, this exercise is a difficult one and prone to subjective elements depending on the person carrying out the analysis. Each step along the way of the “problem-solution approach” aims to take out of the equation this subjective element when assessing inventive step.

While the Boards of Appeal have decided that the application of this approach is not mandatory, they have also repeatedly found that it is the best way of avoiding a subjective ex post facto analysis and therefore in principle the approach should be used. The Boards of Appeal even held that if one exceptionally deviates from this established approach, reasons for deviation must be provided. Furthermore, it is simply a fact that both the departments of first instance of the EPO and the Boards of Appeal in practical life insist on a “problem-solution approach”-analysis when arguing inventive step, whether it is as an applicant during examination proceedings, as a patent proprietor during opposition proceedings or as an opponent. Not following the “problem-solution approach” by the letter is often very much to the detriment of the party involved. Therefore, it is important to familiarize oneself with the general way the “problem-solution approach” works and the peculiarities that come with it.

Navigating the intricacies of the “problem-solution approach” can be a challenging task, even for European patent attorneys, for whom the EPO’s “problem-solution approach” is second nature. Therefore, in the next couple of weeks, I will go in detail through each of the three stages of the “problem-solution approach”, in a series of blog posts at this venue, titled “Navigating the EPO’s “problem-solution approach”—Part I-IV”. Next up: How to find the closest prior art? Stay tuned.

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The Problem and Solution Approach - Basic Case Law and Recent Development (II) epi Information 2/2016." data-html="true">[1]

Michael m. fischer (de), european patent attorney, b. objective technical problem.

As a next step, the distinguishing features between the appropriate starting point and the subject-matter of the claim are determined. Then, the technical effect achieved by these distinguishing features is determined and an objective technical problem is formulated based on the technical effect. It is important to note that the formulated objective technical problem must not provide pointers to the claimed solution. T 641/00 suggests to put all non-technical features into the problem in order to avoid that they provide pointers to the solution." data-html="true">[2] The objective technical problem need not be the subjective technical problem mentioned in the background section of the patent application. Hence, the objective technical problem can be reformulated. If a technical effect cannot be demonstrated, the problem must be reformulated. [3]

Before the EPO, the presence of a technical effect is essential to the acknowledgement of an inventive step. In this context, the decision T 2044/09 should be cited in which the Board noted that "the mere fact that the claimed subject-matter was not novel over the prior art, even when combining document, was not sufficient to render it inventive. In fact in the absence of a proven effect in comparison to the prior art, it was considered that this must be regarded as an arbitrary non-functional modification of the prior art. Even if there was no pointer or suggestion in the prior art towards the addition of a distinguishing feature, if said modification was not linked to a particular functionality, then it could not per se constitute the basis for acknowledging an inventive step".

Hence, when drafting a European patent application, care should be taken to not only mention a technical problem or a technical effect in the background section of the patent application which normally relates to the overall problem addressed in the patent application but also to mention the technical effects associated with features mentioned in the dependent claims and/or in the description. If the technical effect is not mentioned in the application, it may be more difficult to convince the Examining Division that the technical effect (merely alleged in examination proceedings) is actually achieved. Reference is made to GL G-VII, 5.2 which states that "It is also possible to rely on new effects submitted subsequently during the proceedings by the applicant, provided that the skilled person would recognise these effects as implied by or related to the technical problem initially suggested". While it is common practice in the field of pharmacy to file results of clinical studies performed after the filing of the application in order to demonstrate a technical effect, applicants in other technical areas often do not seem to contemplate this option. For example, if the inventor has published - after filing the patent application - an article in which the technical effect is better explained than in the patent application itself, this article can be adduced in order to demonstrate the technical effect before the EPO. "In T 440/91 }} the Board pointed out that R. 27 EPC 1973 did not rule out the possibility of additional advantages - not themselves mentioned in the application as filed but relating to a mentioned field of use - being furnished subsequently in support of patentability for the purposes of Art. 52(1) EPC 1973 , as such advantages did not alter the character of the invention. Thus, the character of the invention was not altered if the technical problem specified in the application as filed was supplemented by such advantages, since the skilled person might consider them on account of their close technical relationship to the original problem (see also T 1062/93 ). The Board made a distinction with regard to the situation in T 386/89 and T 344/89 , where there was no such technical relationship. In T 386/89 the Board had found that the solution to the technical problem derivable from the application as filed was in no way associated with a technical effect subsequently invoked. This additional effect had thus not been taken into consideration. The alleged effect of a described feature could not be taken into account when determining the problem underlying the invention for the purpose of assessing inventive step, if it could not be deduced by the skilled person from the application as filed considered in relation to the closest prior art. Similarly in T 344/89 , the Board had refused to take account of a subsequently invoked technical effect on the grounds that to do so would have altered the character of the invention ( T 532/00 , T 845/02 , T 2179/08 )" th edition, 2013" data-html="true">[4] . If a technical effect is purported that is associated with a range of values, it should be noted that "an effect cannot be retained if the promised result is not attainable throughout the entire range covered by the claimed subject matter. Therefore, the technical problem needed to be redefined in a less ambitious way ( T 626/90 , T 1057/04 , T 824/07 )" th edition, 2013" data-html="true">[5] . Hence, should a first application not include the technical effects associated with individual features, it should be legitimate to incorporate these technical effects - taking into account the restrictions set forth in the decisions above - into the description of a second application to be filed with the EPO and claiming priority from the first application in order to facilitate its prosecution. Since this addition of technical features does not affect the feature combinations recited in the claims, this measure should not jeopardise the validity of the priority claim. A slightly different question is whether the claimed subject-matter solves the problem to be solved. In this context, the Boards held hat "post-published evidence to support that the claimed subject-matter solves the problem to be solved is taken into account if it is already credible from the disclosure in the patent [or patent application] that the problem is indeed solved. In other words, supplementary post-published evidence may not serve as the sole basis to establish that the problem is solved ( T 1329/04 , T 415/11 )" th edition, 2013" data-html="true">[6] .

At this point, it is worthwhile taking a look across the big pond where no other decision has shaken the patent world in recent years more than "Alice Corp. v. CLS Bank International" rendered by the US Supreme Court in 2014. The patents in suit were held to be invalid because the claims were drawn to an abstract idea, and implementing those claims on a computer was not enough to transform that idea into patentable subject matter. In short, this decision may be interpreted in a way that subject-matter (in this case software) is only patentable if it achieves a technical effect. As harsh and consequential http://cdn.theatlantic.com/assets/media/img/posts/2014/11/chart_1-1/5966e14bf.jpg shows that the USPTO issued fewer than half the number after Alice that it had issued per month during the period prior to Alice. At the same time, however, the issuance of other types of software patents rose. ( https://en.wikipedia.org/wiki/Alice_Corp._v._CLS_Bank_International#Lower_courts )" data-html="true">[7] as this decision may (or may not, if overturned) be for the patent world in the USA, it could constitute a harmonisation between the jurisprudence of the USA and the EPO. The author of this article appreciates the EPO's concentration onto a technical effect. Firstly, it makes sure that a patent is granted only for "technical" solutions (which leads, however, to the problem of the meaning of the term "technical"). Secondly, a patent is granted in return to the applicant making the invention public which can then be further developed by others. Hence, if it is not (at least implicitly) clear what the invention achieves because it is nothing but a combination of seemingly arbitrary features, then the description has to be considered to be incomplete and may be of little or no value to the public since the public does not know what the invention is for (see also the requirement of R. 42 (1) (c) EPC).

If the objective technical problem formulated based on the distinguishing features leads to a problem that cannot occur at the selected appropriate starting point, the selected starting point is inappropriate (see T 513/00 ). At least one cannot show in a logical chain of arguments that starting from this document the subject-matter of the claim can be arrived at in an obvious manner. When attempting to show that the subject-matter of a claim is not inventive using the problem and solution approach, it is advisable to countercheck whether the problem formulated is a problem that the selected appropriate starting point actually has. Otherwise the chain of argumentation becomes illogical.

As already mentioned above, if one has chosen a closest prior art document from a different genus, then it is difficult to formulate a reasonable problem which does not point to the solution because the problem would have to be based on the generic difference. If we consider a military helmet having the features a, b and c and the closest prior art is a worker's safety helmet having the same features a, b and c. The problem cannot be formulated as how to modify the safety helmet to also be able in military actions directly points to the solution. How to modify the safety helmet to be usable in a different environment would be too broadly formulated.

This leads to the question on how specific the objective technical problem should be formulated. In T 1019/99 , the Board held that it is established case law that the objective technical problem to be used in the problem and solution approach is to be formulated so that it does not anticipate or contain pointers to the solution. This constrains the specificity of the formulation. However, there is also a constraint on the amount that the formulation can "back off" from this specificity, i.e. a constraint on the generality of the problem. The problem can be no more general than the disclosure of the prior art allows . Otherwise, a problem could be formulated so generally as to circumvent indications in a prior art document towards the claimed solution. Thus the correct procedure for formulating the problem is to choose a problem based on the technical effect of exactly those features distinguishing the claim from the prior art that is as specific as possible without containing elements or pointers to the solution .

A. Obviousness

Following the gedankenexperiment of the problem and solution approach, by determining the appropriate starting point and the objective technical problem, a hypothetical situation is defined in which the fictitious skilled person [8] , a purely fictitious person with a certain knowledge and abilities, could have been.

(Hypothetical) Situation = Appropriate Starting Point + Objective Technical Problem

While the first two steps of the problem and solution approach are made in full knowledge of the invention (i.e. based on hindsight), it is now important to erase the knowledge of the invention from one's mind in order to be able to assess the question of obviousness without hindsight.

In practice, this situation could be compared with a development process in which a development manager gives a development engineer or team of engineers (skilled person(s)) the order to further develop a given product in a certain respect (based on a functional specification). [9] The question is whether the skilled person in the situation above could and would have found the solution to the objective technical problem, for example in a second document from the prior art, or not (could-would approach). Hence, a skilled person may perform the role of a guinea pig by means of which it is tested whether it reaches - in a given situation - the target (the subject-matter of the claim) or not. It is important to note that the skilled person neither selects the closest prior art nor formulates the problem but is presented with both of them.

The assessment of whether the further development of the prior art is obvious or not is not determined by what the skilled person could have done but by what he would have done. It should be noted that it is completely irrelevant in which situation the inventor actually was.

"That it was theoretically possible for the skilled person to arrive at the invention simply means that he could have used the requisite technical means. If, however, it is to be established that he would actually have used them, it must be possible to ascertain a pointer in the prior art which would have prompted him to do so ( T 1317/08 )" th edition, 2013" data-html="true">[10] .

Although the "raising the bar" initiative a few years ago only affected the European Patent Office and not the Boards of Appeal, some Boards of Appeal came to the conclusion that even an implicit prompting or implicitly recognisable incentive is sufficient to show that the skilled person would have combined the elements from the prior art (see  T 257/98 and T 35/04 ). This must have been the case for the skilled person before the filing or priority date valid for the claim under examination.

In T 1014/07 the Board stated that the mere existence of teachings in the prior art is not a conclusive reason for explaining that the skilled person would have combined these teachings in order to solve the problem that he or she is confronted with. As a further reason for denying an inventive step for the claimed subject-matter the examining division indicated that "[t]he mere fact that a known biochemical step has been added to a known chemical process of oxidation cannot be considered in itself inventive in the absence of a special feature or advantage of the combined use of biochemical and chemical processes". However, for the determination of the obviousness or non-obviousness of claimed subject-matter, it is not decisive that teachings are known - it must be decided whether or not the skilled person would have combined the known teachings such as to arrive at the claimed subject-matter when attempting to solve the underlying technical problem. Thus, in contrast to the examining division's view, the combination of known teachings may result in non-obvious subject-matter, namely when the skilled person is not motivated, for example by promptings in the prior art, to make such a combination. Under these circumstances the presence of any special effect arising from the combination is not necessary to establish an inventive step .

While it appears that the "could-would approach" is sometimes only applied to the question whether there was an incentive/prompting to apply the teaching of a secondary document to the teaching of the appropriate starting point, the author of the article suggests the following more comprehensive scheme:

While the question of "could" merely refers to the fact whether something falling under the features of the claimed solution was somewhere available in the prior art, the question of "would" deals with the question whether the skilled person would have found the solution and applied it to the appropriate starting point. In short:

Could : Would = Solution : Context

In other words, "could" refers to the theoretical possibility of finding the solution while "would" denotes whether the skilled person would have practically found the solution in view of the context in which the solution is presented. Typically, the transfer of a known solution in a suitable context to an appropriate starting point is considered to be a further development that the skilled person could and would have achieved. In T 142/84 [12] , the Board argued in a such an archetypal way: "The respondents are of course correct when they state that the mere fact that a skilled person would not encounter insurmountable difficulties in providing a characterising feature of a claim does not lead (necessarily) to the conclusion that there is no inventive step. However, when the feature is known from a document in the same specialised field, and solves the same problem, then the fact that the skilled person would not encounter insurmountable difficulties in applying this known feature to a known apparatus from a second document does demonstrate that the documents are not conflicting (see T 02/81, OJ EPO 10/1982, 401), and that an inventive step is lacking . The problem solved does not have to be stated expressis verbis in the prior art. The respondents refer further to the earlier decision T 39/82 OJ EPO 11/1982, 423. In that case it was decided that the problems to be respectively solved with a known measure in the known case and in the case to be decided must be taken into account. Since the problems differed fundamentally from one another it could not be considered obvious for the skilled person to use this known measure in a different context. Since however the purpose of the features known from US-A-4 100 657 is the same as in the present case, it cannot be denied that the problems do not differ fundamentally and this prior art gave the skilled person an indication for applying these features in the present case."

In yet other words, the could-would approach tests in how far two documents/teachings fit with each other. This is sometimes compared with a jigsaw puzzle [13] with the documents being the pieces of the jigsaw puzzle. As mentioned above, it is crucial that at least one of the documents contains an incentive/prompting so that its teaching will be applied to the teaching of another document which implies that "mosaic-like combinations will normally not be persuasive" http://www.bardehle.com/en/publications/interactive_brochures/inventive_step.html " data-html="true">[14] . However, one must not forget that the prior art can also be represented by a "prior use" which normally - by its nature - does not contain any incentive/prompting.

While the skilled person needs an incentive to apply the teaching of a second prior art item to that of an appropriate starting point, the Guidelines state under G-VII, 6 (iii) that "it would normally be obvious to combine with a prior art document a well-known textbook or standard dictionary; this is only a special case of the general proposition that it is obvious to combine the teaching of one or more documents with the common general knowledge in the art". This obviously means that no incentive/prompting is needed to apply the skilled person's common general knowledge to an appropriate starting point. Thus, according to the Guidelines, the difference between a normal prior art document and the skilled person's common general knowledge appears to be that the common general knowledge as the skilled person's mental furniture is very present in his brain and therefore the hurdle that the skilled person applies it to a teaching of another document is very low or not existing (= no incentive is needed). However, care has to be taken in order to identify what is actually known from the common general knowledge and how the skilled person would apply it to the teaching of a prior art document. It is important to note that the skilled person's common general knowledge may not be applied in a certain (target-oriented, purposeful) direction to arrive at the claimed subject-matter. This would be considered an unallowable ex-post-facto analysis.

In T 1471/11 , the Board held that "the argument of the appellant must fail that neither claim 1 nor the description of the patent in suit define the claimed arrangement for lubrication to such an extent that it can be understood without having recourse to the general technical knowledge and understanding of the skilled person. With that general technical knowledge in mind, in addition to the teaching of the available documents, the examination of inventive step would necessarily lead to the conclusion that the claimed subject-matter does not involve an inventive step. The reason is that even if it is correct that general technical knowledge and practice needs to be taken into account in order to reduce the arrangement for lubricating defined by claim 1 to practice, the decisive direction in which this general technical knowledge is to be applied to arrive at what is claimed, still needs to be derivable from some teaching or knowledge" [15] . The Board set forth a similar argumentation in T 386/12 and T 1426/10 .

This is different from the use of the common general knowledge in the field of "sufficiency of disclosure" (Art. 83 EPC) where the skilled person would use his common general knowledge in a target-oriented way to determine whether the invention is sufficiently disclosed by the application as a whole. He is in the position to use his common general knowledge in a target-oriented way because he knows the prior art and the invention, while the skilled person in the assessment of inventive step only knows the prior art. However, in both assessments, "the same level of skill has to be applied ( T 60/89 and T 373/94 )" th edition, 2013" data-html="true">[16] . In slightly other words: "The skilled person when assessing sufficiency of disclosure of a patent has knowledge of the invention as disclosed, i.e. knowledge of both the prior art, the problem and its solution, and is aware of documents cited in the patent and the common general knowledge in the art" ( T 6/84 , T 171/84 ) st edition, 2013, p.174, section 2.2" data-html="true">[17] . With both decisions being quite old and search engines becoming more and more powerful, it would be interesting to see if e.g. a novel, unusual or special term in a claim of a patent application, the term not being part of the skilled person's common general knowledge (i.e. cannot be found in standard textbooks, etc.) and the patent application neither containing any explanations nor references to other documents, would make the application not meet the requirement of "Sufficiency of Disclosure" even if an explanation of the term could easily be found using a search engine. The decision T 580/88 also appears to be quite harsh in this respect.

In T 1641/11 , the Board held that the assertion that something was part of the common general knowledge therefore needed only to be substantiated if challenged by another party or the EPO. "Where an assertion that something was part of the common general knowledge is challenged, the person making the assertion must provide proof that the alleged subject-matter indeed forms part of the common general knowledge ( T 438/97 , T 329/04, T 941/04 , T 690/06 )" th edition, 2013" data-html="true">[18] .

D. Further Considerations

The following schematic example wants to demonstrate why it does not make sense to focus on one closest prior art document.

(The lowercase letters denote special features that anticipate the features denoted by the corresponding uppercase letters.)

Both documents D1 and D2 qualify as appropriate starting points (same purpose as the claim, etc.). However, since D2 has one more feature in common with the claim, it could be considered to be the (one and only) closest prior art document. Although D2 is per se closer to the claim than D1, it may be that there are incompatibilities (e.g. mechanical incompatibilities, incompatible dimensions) between D2 and D3 and D2 and D4 such that the skilled person would neither apply the teaching of D3 nor the teaching of D4 to that of D2. Hence, the (wrong) conclusion would be that starting from the closest prior art D2, the skilled person would not have arrived at the subject-matter of the claim in an obvious manner. However, there may not be incompatibilities between document D1 and D3 and the skilled person could and would apply the teaching of D3 to that of D1, thereby arriving at the subject-matter of the claim in an obvious manner. Since there exists one way to arrive at the subject-matter of the claims, it has been shown that claim 1 does not involve an inventive step. Since the question whether one arrives at the subject-matter of the claim in an obvious way also depends on how well the primary reference fits together with the secondary reference, documents must not be prematurely disregarded as appropriate starting points.

Applying the problem and solution approach is sometimes compared with mountaineering http://k-slaw.blogspot.de/2012/09/t-5609-so-close.html " data-html="true">[19] . Two hikers A and B, of ordinary skill, not Reinhold Messner, (person of ordinary skill in the art, no Nobel Prize winner) want to hike to the summit (invention/ subject-matter of claim) of Mount Inv. From their starting point, they both see the summit they want to reach (selection of appropriate starting point is made in knowledge of the invention). Hiker A takes a trail (a first appropriate starting) which is very steep and goes very straight into the direction of the summit (same purpose). This trail appears to be very promising since, as far as he can see, it almost reaches the summit (only one feature missing ☺ ). Hiker B takes another trail (a second appropriate starting point) which also goes in the direction of the summit but is less steep. However, he can only see that his trail ends somewhere in the forest at half the height of the summit (some more features missing ☹ ). When hiker A reaches the end of his trail, he notices that the trail abruptly ends and that he would have to climb (perform an inventive step) the last few meters from there to reach the summit. Unfortunately, there is no signpost (pointer, incentive/prompting) showing him how he could alternatively reach the summit by hiking. He also looks into his standard mountain survival guide (common general knowledge - a hiking map would not be a good analogon under the assumption that the common general knowledge must not be used target-oriented) that he always carries with himself. When hiker B reaches the end of his trail, he has only reached half the height of the summit, but he notices a signpost (pointer to another document) that indicates that several other trails (further documents possibly containing a solution) start from a place very close (neighboring technical field) from here. He follows the signpost and arrives at a point where he sees different signposts (incentives/promptings to different documents), one of them (incentive/prompting to the document disclosing the solution) indicating that this hiking trail - ideal for the ordinary hiker, no climbing necessary - leads to the summit of the mountain. The hiker follows this trail (second document) and easily arrives at the summit without any climbing. A trail which appears at first glance less promising than another trail may lead to the summit while the other trail may not. In the language of the problem and solution approach, this means that not any document that appears to come closer to the subject-matter of the claim than all other documents is suitable to show that the subject-matter of the claim is inventive, while a not so close document is ideally complemented by another document which shows that the subject-matter of the claims is indeed inventive.

E. Alternatives

The EPO lives and breathes the problem and solution approach. Hence, the decision T 465/92 received a lot of attention because already its headnote stated that the problem and solution approach is no more than one possible route for the assessment of inventiveness. Accordingly, its use is not the only possibly approach when deciding on inventiveness under Article 56 EPC. In the Case Law Book 6 th edition, this decision has been classified as "a one-off decision". Interestingly, in the 7 th edition, this remark has been replaced with the sentence that the Board "took the view that all of the seven cited documents came equally close to the invention". Possibly, this decision, which has often been categorized as a heretical decision not to be followed, was an early decision to recognize the issue of referring to one closest prior document, which was not possible in the present case, and therefore decided not to apply the problem and solution approach. Possibly, the members of the Board had a (formal) problem with the superlative notion of a one and only "closest prior art document" and therefore declined applying the problem and solution approach. Maybe, the amendment of the Case Law Book is a late and silent rehabilitation of this decision which partly anticipated the decisions T 967/97 , T 558/00 , T 21/08 , T 308/09 and T 1289/09 that have now found their way into the last version of the Guidelines.

In T 939/92 the Board of Appeal referred to the decision T 465/92 . Although it was held in No. 9.1 of the reasons of this decision that the "problem and solution approach" is not a sine qua non for the determination of inventiveness by the EPO, it follows, in the Board's judgment, from the detailed explanations given in the following points 9.2 to 9.6 of the reasons that in that case the Board refrained from identifying a certain document as "closest state of the art" and formulating a "technical problem" on the basis of such a state of the art. In the present case, however, the question of selecting a particular document as "closest state of the art" is not at issue. However, in decision T 465/92 the Board considered the results which had been objectively achieved by the claimed invention, and then proceeded, on that basis, to decide whether or not the cited state of the art, as a whole, would have suggested to the skilled person that these results could be achieved in the way indicated in the patent under consideration.

In T 188/09 the Board stated that the "problem and solution approach" is regularly applied as an auxiliary means by the instances of the European Patent Office in the course of deciding whether or not claimed subject-matter fulfils the requirements of Article 56 EPC. The appellant, referring to decision T 465/92 of 26 November 1993, observed that there are however cases where the "problem and solution approach" hinders, rather than assists answering the question of whether claimed subject-matter is obvious over the prior art.

In decision T 465/92 the Board explicitly decided not to use the "problem and solution approach" (see points 6 to 9.6 of the Reasons). Thus, the Board understands the appellant's reference to this decision as an argument that the present case is one where the "problem and solution approach" should not be used.

The Board notes first that whatever approach is applied as an auxiliary means for the evaluation of inventive step of claimed subject-matter, in a given evidential situation it must provide the same result, be it either in favour of or against inventive step. Therefore, in the present case, even if the "problem and solution approach" was applied, the decision on inventiveness should be the same as if it was not used.

Moreover, according to the reasons of decision T 465/92 , the Board decided to avoid the "problem and solution approach" because it considered that the seven relevant citations were all equally close to the claimed invention and that therefore, the opponent "ought not to be tied down by having to select one or more citations as being closer than others" (see points 9.3 and 9.4 of the Reasons). Consequently, the Board considered them all individually without selecting one as the closest prior art document .

The Board in decision T 465/92 also notes in point 9.5 of the Reasons that there may be situations which "can result in a complicated multi-step reasoning where the facts were clear, either for or against inventiveness. Thus, if an inventions breaks new ground it may suffice to say that there is no close prior art rather than constructing a problem based on what is tenuously regarded as the closest prior art."

None of the circumstances for the avoidance of the classical "problem and solution approach" referred to in decision T 465/92 is present in the case at hand [i.e. **T 188/09**], i.e. neither can the claimed subject-matter be considered as breaking new ground, since document D4 describes a G-protein coupled receptor specifically located in taste cells nor is there a large number of equally close prior art documents (see points 9 to 13 below).

Thus, having considered the rationale in decision T 465/92 the present Board does not see a reason to apply the approach adopted by the Board in that decision rather than the classical "problem and solution approach".

F. Conclusion

The application of the problem and solution approach has evolved over the years. However, the problem and solution approach is still - and more than ever - the one and only prayer before the EPO and has pushed all other approaches into the field of heresy. The problem and solution approach is even applied outside the scope of the EPC since the PCT International Search and Preliminary Examination Guidelines also suggest applying this approach http://www.wipo.int/export/sites/www/pct/en/texts/pdf/ispe.pdf " data-html="true">[20] . Although the problem and solution approach appears to be algorithmic [21] in nature and hundreds of decisions of the Boards of Appeals give advice on how to apply the approach in many cases, its outcome is in the eyes of the author of this article not always predictable. Ultimately, the question of "inventive step" is a legal question and assessing inventive step is an act of judging which involves subjective elements. In patent law and in many other legal fields the roman legal principle "Iudex non calculat." still applies. Nevertheless, the problem and solution approach is a systematic approach and that alone may be the reason for its success and longevity.

Any feedback is welcome and can be sent to [email protected] or [email protected]

• This is the second part of an article that is based on a talk held by the author on September 8, 2015 at the European Patent Experts' Forum (EuPEX) in Munich. The first part was published in epi Information 2/2016.
• T 641/00 suggests to put all non-technical features into the problem in order to avoid that they provide pointers to the solution.
• Handout of presentation "Problem/Solution Approach to Inventive Step and Challenging Cases" held by Graham Ashley, Chairman of a Technical Board of Appeal, at the conference "Boards of Appeal and key decision" on November 26/27, 2015 in Munich
• Case Law of the Boards of Appeal, section I.D, 4.4.2, 7 th edition, 2013
• Case Law of the Boards of Appeal, section I.D.4.6, 7 th edition, 2013
• The graph available at http://cdn.theatlantic.com/assets/media/img/posts/2014/11/chart_1-1/5966e14bf.jpg shows that the USPTO issued fewer than half the number after Alice that it had issued per month during the period prior to Alice. At the same time, however, the issuance of other types of software patents rose. ( https://en.wikipedia.org/wiki/Alice_Corp._v._CLS_Bank_International#Lower_courts )
• A detailled definition of the skilled person, his abilities and his knowledge in different fields of technology is omitted. Not many decisions on this seem to have been issued any time recently.
• Hoekstra, J., "Methodology for Paper C - Training for the European Qualifying Examination", Deltapatents, October 2009, p.151
• Case Law of the Boards of Appeal, section I.D.5, 7 th edition, 2013
• Of course, the question whether two teachings are compatible with each other is determined based on the concrete disclosure of the two documents and not on the abstraction level of the claims since the skilled person does not know the subject-matter of the claim.
• Hoekstra, J., "Methodology for Paper C - Training for the European Qualifying Examination", Deltapatents, October 2009, p.154 and cover page
• section 3.3 of http://www.bardehle.com/en/publications/interactive_brochures/inventive_step.html
• The Federal Court of Justice of Germany came to a similar (possibly even broader) conclusion in its decision Xa ZR 56/05 "Airbag-Auslösesteuerung": "The mere fact that a teaching belongs to the skilled person's common general knowledge does not yet prove that it was obvious for the skilled person to employ this teaching in order to solve a specific technical problem". A further decision in this context is the decision X ZR 139/10 "Farbversorgungssystem" in which the Federal Court of Justice came to the conclusion that the skilled person would have applied a solution from his common general knowledge "because using its functionality was objectively expedient and there were no special circumstances rendering such use impossible, difficult or otherwise impracticable from a specialist point of view".
• Case Law of the Boards of Appeal, section I.D.8.3, 7 th edition, 2013
• Visser, D., "The Annotated European Patent Convention", 21 st edition, 2013, p.174, section 2.2
• Case Law of the Boards of Appeal, Section I.D.8.3, 7 th edition, 2013
• see for instance: http://k-slaw.blogspot.de/2012/09/t-5609-so-close.html
• "One specific method of assessing inventive step might be to apply the so called "problem-solution approach", PCT International Search and Preliminary Examination Guidelines as in force from October 1, 2015, Appendix to Chapter 13, page 117, http://www.wipo.int/export/sites/www/pct/en/texts/pdf/ispe.pdf
• Not surprising in view of the high number of scientifically educated people in patent law. Not surprising either if the search tools used by the EPO Examiners already supported the problem and solution approach by e.g. suggesting documents from the same, broader or neighbouring technical fields which in combination anticipate all the features of a claim.

Existence of Solutions for p ( x )-Laplacian Elliptic BVPs on a Variable Sobolev Space Via Fixed Point Theorems

• Open access
• Published: 13 May 2024
• Volume 23 , article number  195 , ( 2024 )

Cite this article

You have full access to this open access article

• Souad Ayadi 1 ,
• Jehad Alzabut 2 , 3 ,
• Hojjat Afshari 4 &
• Monireh Nosrati Sahlan 4  

In this paper, we prove some existence theorems for elliptic boundary value problems within the p ( x )-Laplacian on a variable Sobolev space. For this purpose, the main problem is transformed into a fixed point problem and then fixed point arguments such as Schaefer’s and Schauder’s theorems are used. Our approach involves fewer stringent assumptions on the nonlinearity function than the prior findings. An interesting example is presented to examine the validity of the theoretical findings.

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1 Introduction

The study of differential equations and variational problems involving non-standard p -growth conditions has attracted special attention. Such problems often arise in the modeling of several phenomena such as electrorheological fluids, image restoration, magnetostatics problems, and many other problems in elastic mechanics [ 33 , 36 , 46 ]. Due to their widespread applications, the investigation of nonlinear elliptic boundary value problems involving the p ( x )-Laplacian operators have been reported using different approaches [ 1 , 5 , 13 , 16 , 18 , 25 , 26 , 39 , 42 , 43 , 44 ]. Meanwhile, there have been many authors who focused their works on the study of the equations involving the p ( x )-Laplacian operators and obtained some important results; the reader can consult the papers [ 4 , 7 , 15 , 17 , 20 , 21 , 22 , 27 , 29 , 30 , 34 , 35 ].

On the other hand, the notion of variable exponent Lebesgue spaces introduced by Orlicz in the paper [ 31 ]. In [ 46 ], Zhikov presented a new direction of investigation, which created the relationship between spaces with variable exponent and variational integrals under nonstandard growth conditions. Some interesting results concerning the generalized Lebesgue spaces and the generalized Lebesgue–Sobolev spaces can be found in [ 8 , 9 ], and references therein.

Recently in [ 40 ], Vetro investigated a nonlinear p ( x )-Kirchhoff type problem with the Dirichlet boundary condition, in the case of a reaction term depending on the gradient (convection). Utilizing a topological attitude based on the Galerkin method, he studied the existence of two notions of solutions: strong generalized solutions and weak solutions. Further, the authors in [ 46 ] used minimax approaches in conjunction with the Trudinger-Moser inequality to investigate a particular kind of the weighted Kirchhoff problem and found some existence results of a solution in the subcritical exponential growth situation with positive energy. For more information in this area refer to [ 14 , 17 , 20 , 41 ]. Yet, in the event that the Catheodory reaction is gradient dependent, some approximation methods such as the Galerkin method are regarded as essential resources for understanding the p ( x )-Laplace equation since the problem loses its variational character in this scenario. In [ 38 ], Sousa studied a version of the abstract lower and upper-solution method for some operators. Indeed, he presented, the existence of a positive solution for a new class of fractional systems of the Kirchhoff type with \(\psi \) -Hilfer operators via the method of sub and supersolutions.

Motivated by the results of the above-mentioned work, we prove some existence results of solutions for elliptic boundary value problems with p ( x )-Laplacian of the following form

and \(\Omega \) is a smooth bounded domain in \( \mathbb {R}^{N} (N\ge 2)\) , \( p(x)\in C(\overline{\Omega })\) is \(\log \) -Hölder continuous with values in \( (1, +\infty )\) , and \( f: \Omega \times \mathbb {R}\longrightarrow \mathbb {R}\) is a Carathéodory function, satisfying some growth conditions [ 12 ]. Problem ( 1.1 ) naturally describes applications in fluid mechanics and thus it is of a great significance for engineers and scientists. Fixed point arguments based on Schaefer’s and Schauder’s fixed point theorems as well as the method of sub-supersolution are used for proving the main theorems. Indeed, the existence results of the weak solutions for the p -Laplacian BVPs have been established in [ 19 , 23 , 28 ], while the variational and topological methods were used in [ 6 , 11 , 32 , 45 ], and the simple variational arguments based on the Mountain-Pass theorem was used in [ 28 ]. The structure of the nonlinearity f in ( 1.1 ) suggests that the assumptions made about it are less restrictive than in previous discoveries. The paper discusses major findings within the variable exponent Sobolev space, as well as via utilizing fundamental properties of the p ( x )-Laplacian and Nemytskii operators.

The article is structured as follows. Section 2 presents some fundamental concepts which are essential to prove the results in the next sections. The main results together with an interesting example are explicitly delivered in Sects. 2 and 3 . A brief conclusion is given in Sect. 4 .

2 Preliminary Results

Here, we present some essential results on the variable exponent Sobolev space and state some basic properties of the p ( x )-Laplacian and Nemytskii operators. For more details, we orient the reader to [ 8 , 9 , 12 , 19 , 23 , 28 ].

Let \(\Omega \subset \mathbb {R}^{N} (N\ge 2)\) be an open bounded subset with smooth boundary \( \partial \Omega \) and set

For \(p\in C_{+}(\overline{\Omega })\) , we define

Clearly, \(1< p^{-}\le p^{+}<\infty ,\) and

We define the Luxemburg norm by:

Further, \( \left( L^{p(x)}(\Omega ), \Vert \jmath \Vert _{p(x)}\right) \) are Banach spaces which are reflexive if and only if \(1< p^{-}\le p^{+} <\infty . \) Due to the inclusion of the Lebesgue spaces, we get: if \( 0<|\Omega |<\infty \) and \(p_1(\cdot )\) , \(p_2(\cdot )\) are variable exponents such that \(p_1(x) \le p_2(x)\) a.e. \( x \in \Omega \) , then, there exists a continuous embedding \(L^{p_2(x)}(\Omega )\hookrightarrow L^{p_1(x)}(\Omega ).\)

Moreover, if \(L^{p'(x)}(\Omega )\) is the conjugate space of \(L^{p(x)}(\Omega ),\) where \(\frac{1}{p(x)}+\frac{1}{p^{\prime }(x)}=1\) , then:

In the sequel, we employ the modular and its properties, which is \(\sigma _{p(x)}:L^{p(x)}(\Omega )\rightarrow \mathbb {R}\) , defined by

It should be noticed that the \(\log \) –Hölder continuous and Carathéodory functions are defined as follows.

Definition 2.1

The variable exponent p ( x ) is \(\log \) –Hölder continuous if there exists \(C > 0\) with

for \(x,y\in \mathbb {R}^{N}\) , and \(\Vert x-y\Vert \le \frac{1}{2}.\)

Definition 2.2

A function \(f: \Omega \times \mathbb {R}\longrightarrow \mathbb {R}\) is Carathéodory function, if \(f(.,\eta )\) be measurable on \(\mathbb {R}\) and \(f(\xi ,.)\) is continuous on \(\mathbb {R}\) .

Proposition 2.3

[ 12 ] For all \(\jmath , v\in L^{p(x)}(\Omega )\) , we have

It follows that

Definition 2.4

The variable Sobolev space \( W^{1,p(x)}(\Omega )\) is defined as follows

with the norm

The closure of \(C_{0}^{\infty }(\Omega )\) in \( W^{1,p(x)}(\Omega )\) is denoted by \( W_{0}^{1,p(x)}(\Omega )\) , and we define

Definition 2.6

Suppose \(\Gamma \) and \(\Lambda \) be real Banach spaces, \(S \subset \Gamma \) be nonempty and the symbols \(\rightharpoonup \) and \(\rightarrow \) denotes the weak and strong convergence, respectively. The mapping \(\mathcal {L}:S\rightarrow \Lambda \) is called bounded if the projection of any bounded set in \(\Gamma \) under \(\mathcal {L}\) be a bounded set in \(\Lambda \) .

Definition 2.7

Suppose \(\Gamma \) be a real reflexive Banach space, \(\Gamma ^{*}\) be its dual and \(S \subset \Gamma \) be nonempty. A mapping \(\mathcal {L}:S\rightarrow \Gamma ^{*}\) is said to be of class \((S_{+})\) , if for any \(\left\{ \gamma _{n}\right\} \) in \(\Gamma \) , where \(\gamma _{n}\rightharpoonup \gamma \) and \(\overline{lim} \left\langle \mathcal {L}(\gamma _{n}),\gamma _{n}-\gamma \right\rangle \le 0\) , we can conclude that \(\gamma _{n}\rightarrow \gamma \) .

Proposition 2.8

The spaces \( W^{1,p(x)}(\Omega )\) and \( W_{0}^{1,p(x)}(\Omega )\) are separable reflexive Banach spaces.

If \(\gamma \in C_{+}(\overline{\Omega })\) and \(\gamma (x) < p^{*}(x) \) for \( x \in \overline{\Omega },\) then the embedding from \( W^{1,p(x)}(\Omega )\) to \(L^{\gamma (x)}(\Omega )\) is continuous and compact.

There exists \(\vartheta _{0} > 0, \) with

which implies that, \( \Vert \nabla \jmath \Vert _{p(x)}\) and \(\Vert \jmath \Vert _{1,p(x)}\) are equivalent norms on \(W_{0}^{1,p(x)}(\Omega )\) .

The Nemytskii operator will play an essential role in the subsequent discussion.

Proposition 2.9

([ 19 ]) Let \(f: \Omega \times \mathbb {R} \rightarrow \mathbb {R} \) be a Carathéodory function and satisfies the growth condition

where \( p_{1}(.), p_{2}(.) \in C_{+}(\overline{\Omega }), g \in L^{p_{2}(x)}(\Omega )\) and \(a \ge 0\) is a constant. Then the Nemytskii operator \(N_{f}\) satisfies:

\(N_{f}\left( L^{p_{1}(x)}(\Omega )\right) \subset L^{p_{2}(x)}(\Omega ),\)

\(N_{f}\) is continuous from \( L^{p_{1}(x)}(\Omega ) \) to \(L^{p_{2}(x)}(\Omega ),\)

\(N_{f}\) maps bounded set into bounded set.

Further, it is important to review the properties of p ( x )-Laplacian operator. We consider the following functional \(\varphi \) defined by

Here \(\varphi \) is continuously Fréchet differentiable and \(\varphi '(\jmath ) = -\Delta _{p(x)}\jmath , \) for all \( \jmath \in W_{0}^{1,p(x)}(\Omega )\) where

where, \( \widetilde{W}_{0}^{1,p(x)}(\Omega )\) is a dual space of \( W_{0}^{1,p(x)}(\Omega ).\)

Proposition 2.10

[ 12 ] The mapping \(- \Delta _{p(x)}:\,W_{0}^{1,p(x)}(\Omega ) \longrightarrow \widetilde{W}_{0}^{1,p(x)}(\Omega )\) satisfies the following:

\(- \Delta _{p(x)}\) is a homeomorphism from \( W_{0}^{1,p(x)}(\Omega )\) to \( \widetilde{W}_{0}^{1,p(x)}(\Omega )\) ;

\( - \Delta _{p(x)}\) is a continuous, bounded and monotone operator;

\( - \Delta _{p(x)}\) is a mapping of type \( S_{+}\) ;

The operator \( - \Delta _{p(x)}\) has a continuous inverse mapping \( \left( - \Delta _{p(x)}\right) ^{-1} :\,\widetilde{W}_{0}^{1,p(x)}(\Omega ) \longrightarrow W_{0}^{1,p(x)}(\Omega )\) ;

\( \left( - \Delta _{p(x)}\right) ^{-1}\) is bounded and satisfies the \( S_{+}\) condition.

The proofs of (i–iii) are given in literature. We only prove (iv) and (v).

Proof of (iv). Suppose \(\beta _{n}, \beta \in \widetilde{W}_{0}^{1,p(x)}(\Omega )\) , and \(\beta _{n} \rightarrow \beta \) . Let \(\alpha _{n}=\left( -\Delta _{p(x)}\right) ^{-1}\left( \beta _{n}\right) \) and \(\alpha =\left( -\Delta _{p(x)}\right) ^{-1}\left( \beta \right) \) , then it’s obvious that \( -\Delta _{p(x)}\left( \alpha _{n}\right) =\beta _{n}\) and \( -\Delta _{p(x)}\left( \alpha \right) =\beta \) , thus \(\left\{ \alpha _{n} \right\} \) is bounded in \(W_{0}^{1,p(x)}(\Omega )\) . If \(\alpha _{n} \rightarrow \alpha ^{*}\) , then

considering that \(-\Delta _{p(x)}\) is of type \(S_{+}\) and \(\alpha _{n} \rightarrow \alpha ^{*}\) , we conclude that \(\alpha _{n} \rightarrow \alpha \) . Therefore \(\left( -\Delta _{p(x)}\right) ^{-1}\) is continuous.

Proof of (v). Due to the continuity of \(\left( -\Delta _{p(x)}\right) ^{-1}\) , it is clear that it is bounded. Now we show that \(\left( -\Delta _{p(x)}\right) ^{-1}\) is of type \(S_{+}\) . Suppose \(\beta _{n} \in \widetilde{W}_{0}^{1,p(x)}(\Omega )\) and \(\beta _{n} \rightharpoonup \beta \) , so there exist \(\alpha _{n}, \alpha \in W_{0}^{1,p(x)}(\Omega )\) such that \(\left( -\Delta _{p(x)}\right) ^{-1}\beta _{n}=\alpha _{n}\) and \(\left( -\Delta _{p(x)}\right) ^{-1}\beta =\alpha \) and \(\alpha _{n}\rightharpoonup \alpha \) , that is, \(\left( -\Delta _{p(x)}\right) \alpha _{n}=\beta _{n}\) and \(\left( -\Delta _{p(x)}\right) \alpha =\beta \) . Further, assume that \(limsup_{n\rightarrow \infty } \left\langle \left( -\Delta _{p(x)}\right) ^{-1}\beta _{n},\beta _{n}-\beta \right\rangle \le 0\) , so we get

Since \(-\Delta _{p(x)}\) is of type \(S_{+}\) , we conclude that \(\alpha _{n} \rightarrow \alpha \) . By the continuity of \(\left( -\Delta _{p(x)}\right) ^{-1}\) , we get \(\alpha _{n} \rightarrow \alpha \) . \(\square \)

We close this section with recalling some important fixed point theorems.

Theorem 2.11

(Classical Schaefer’s fixed point theorem [ 37 ]) Let \( T:X\rightarrow X\) a continuous function which is compact on each bounded subset of X . Then, either \( \jmath = \lambda T\jmath \) has a solution for \( \lambda = 1\) , or the set of all such solutions \(\jmath \) , ( \( 0< \lambda < 1 \) ) are unbounded.

Theorem 2.12

(Schauder’s fixed point theorem [ 2 , 3 ]) Let D be a closed and convex subset of a normed linear space X . Then every compact, continuous map \( T:\; D\longrightarrow D\) has at least one fixed point.

3 Main Results

Let \( I_{1} \) be the embedding of \( W_{0}^{1,p(x)}(\Omega )\) into \(L^{\eta (x)}(\Omega )\) and \( I_{2}\) the embedding of \( L^{\delta (x)}(\Omega ) \) into \(\widetilde{W}_{0}^{1,p(x)}(\Omega )\) which is the dual space of \( W_{0}^{1,p(x)}(\Omega ).\) We recall that \( \delta (x)\) is the conjugate of \(\eta (x).\) Let \( F:\; L^{\eta (x)}(\Omega )\ \longrightarrow \ L^{\delta (x)}(\Omega )\) be the Nemytskii operator defined by \( F\jmath (x) = f(x,\jmath (x))\) and \( \overline{F}:\; W_{0}^{1,p(x)}(\Omega )\longrightarrow \widetilde{W}_{0}^{1,p(x)}(\Omega ),\) defined by

be the operator given by

We transfer problem ( 1.1 ) into a fixed point problem of some operators. One can easily see that u is a solution of problem ( 1.1 ) if only if

Let \(\vartheta _{0} \) be such that \( \Vert \jmath \Vert _{p(x)}\le \vartheta _{0}\Vert \nabla \jmath \Vert _{p(x)}, \; \jmath \in W_{0}^{1,p(x)}(\Omega )\) and \( \vartheta _{1} \) the constant of the embedding of \( L^{p(x)}(\Omega ) \; \text{ into }\; L^{\eta (x)}(\Omega ).\) We make use of the following assumptions:

\(|f(x,s)|\le \zeta (x) + c|s|^{\eta (x)-1}\; \text{ where }\; c>0,\, \eta (x) \in C_{+}(\overline{\Omega }), \;\eta (x) < p^{*}(x), \; \forall (x,s) \in \Omega \times \mathbb {R}, \) with \(1< \wp ^{-} \le \wp (x)\le \wp ^{+} < p^{-}, \frac{1}{\wp (x)} +\frac{1}{\delta (x)}= 1,\;\; \zeta (x)\in \left( L^{\delta (x)}(\Omega )\cap L^{p'(x)}(\Omega )\right) ,\)

\(0<c<\dfrac{1}{2\kappa ^{p^{+}-1}\left( \vartheta _{0}\vartheta _{1}\right) ^{p^{-}} }, \; \text{ and }\; \Vert \zeta \Vert _{p'(x)}<\dfrac{1}{2\vartheta _{0}\kappa ^{p^{+}-1}} -c\vartheta _{0}^{p^{-}-1}\vartheta _{1}^{p^{-}},\;\text{ for } \text{ some }\; \kappa \; \text{ in }\; \left[ 0\;1 \right] ,\) where \(p'(x)\) is the conjugate of p ( x ).

Theorem 3.1

Under the assumptions \(A_1\) and \(A_2\) , problem ( 1.1 ) admits at least a non-trivial solution in \(W_{0}^{1,p(x)}(\Omega ).\)

To complete the proof, we split the process into three parts: the operator T is well defined, T is compact and the set \( B = \left\{ {\mathrm{{\jmath }} \in W_0^{1,p(x)} (\Omega ):\;\mathrm{{\jmath }} = \kappa T\mathrm{{\jmath }},\;\kappa \in \left[ {0\;1} \right] } \right\} \) is bounded.

T is well defined. It is clear that the operator    \( T:\, W_{0}^{1,p(x)}(\Omega )\overset{\overline{F}}{\longrightarrow } \widetilde{W}_{0}^{1,p(x)}(\Omega ) \overset{(-\Delta _{p(x)})^{-1}}{\longrightarrow } W_{0}^{1,p(x)}(\Omega ) \) is well defined;

T is compact. Let \( (\jmath _n)\) be a bounded sequence in the reflexive space \( W_{0}^{1,p(x)}(\Omega ).\) Then, there exist \( \jmath _0\) and a subsequence which we also denote \( (\jmath _n)\) that \( \jmath _n \) converge weakly to \(\jmath _0 \) in \( W_{0}^{1,p(x )}(\Omega ).\) By the strong continuity of \( \overline{F}\) (Lemma 2.7, [ 28 ]), we have \( \overline{F}(\jmath _n) \longrightarrow \overline{F}(\jmath _0)\) in \(\widetilde{W}_{0}^{1,p(x)}(\Omega ). \) By the continuity of the operator \( (-\Delta _{p(x)})^{-1} \) (according to the fourth assertion in Proposition 2.10 ), we have \((-\Delta _{p(x)})^{-1}\overline{F}(\jmath _n) \longrightarrow (-\Delta _{p(x)})^{-1}\overline{F}(\jmath _0),\) that is, \( T(\jmath _n)\longrightarrow T(\jmath _0);\)

The set B is bounded. In fact, we prove that for \(\jmath \in B\) , there exists \(R> 0 \; \text{ with }\; \Vert \nabla \jmath \Vert _{p(x)} \le R. \) Considering \( \jmath \in B\) , we have two cases.

If \( \Vert \nabla \jmath \Vert \le 1, \) then B is bounded.

If \( \Vert \nabla \jmath \Vert > 1, \) then by using modular’s properties, we proceed as follows: for \( \jmath = \kappa T\jmath \) , and assuming \(\kappa \ne 0, \) we have \( \dfrac{\jmath }{\kappa }= T\jmath = (-\Delta _{p(x)})^{-1} \overline{F}\jmath .\) Therefore,

and consequently,

Using Hölder–type inequality, propositions 2.3 – 2.8 and the embedding of \( L^{p(x)}(\Omega ) \) into \( L^{\eta (x)}(\Omega )\) , we have

Furthermore, we get

Therefore, we obtain

From assumption \(A_2\) ; \(\Vert \zeta \Vert _{p^{\prime }(x)}<\frac{1}{2v_0\kappa ^{p^{+}-1}}-c{v_0}^{p^{-}-1}{v_1}^{p^{-}}\) , hence by multiplying the both sides of this inequality in \(2v_0\kappa ^{p^{+}-1}\) we get

That is, B is bounded.

By Schaefer’s fixed point theorem, the operator T has a fixed point \( \jmath \) which is the solution of ( 1.1 ). \(\square \)

For our purpose, we consider the following associated problem to ( 1.1 )

Our approach is based on the principle of the sub-super-solution for which the reader can consult [ 10 , 24 ]. By the sub-solution and the super-solution of ( 3.1 ), where, \(\vartheta , \nu \in W_{0}^{1,p(x)}(\Omega ) \) satisfying

We assume the following conditions:

There exist a subsolution \(\vartheta \in W_{0}^{1,p(x)}(\Omega )\) and a supersolution \(\nu \in W_{0}^{1,p(x)}(\Omega ) \) of ( 3.1 ) with \(\vartheta \le \nu . \)

For fixed \( x \in \Omega , \; f(x,s)\) is a nondecreasing function of s for \(\vartheta (x)\le s\le \nu (x).\)

Theorem 3.2

Under the assumptions \( A_1, A_3\) and \( A_4\) , ( 1.1 ) has at least one solution.

Consider the subset \( D \subset W_{0}^{1,p(x)}(\Omega ) \) defined as follow

The proof will be completed in several steps.

D is convex. For \( \jmath , w \in D \) and \( t \in \left[ 0, 1\right] \) , it is clear to see that \( t\jmath + (1 - t)w \in D.\)

D is closed. If \( (\jmath _n)\) be a sequence in D which converge to \( \jmath _0\) in \(W_{0}^{1,p(x)}(\Omega ).\) Then, \( \jmath _n \longrightarrow \jmath _0 \) in \( L^{p(x)}(\Omega ).\) Therefore, there exists a subsequence also denoted \( (\jmath _{n}) \in L^{p(x)}(\Omega ) \) and \(\psi \in L^{p(x)}(\Omega )\) with \( \jmath _n(x) \longrightarrow \jmath _0(x)\) and \( |\jmath _n(x)| \le \psi (x), \, a.e., x \in \Omega .\) Since \( \vartheta (x) \le \jmath _n(x) \le \nu (x),\) passing to the limit when \(n\rightarrow \infty \) , we get \(\vartheta (x) \le \jmath (x) \le \nu (x),\) and hence \(\jmath \in D\) .

\( T:\; D \overset{\overline{F}}{\longrightarrow } \widetilde{W}_{0}^{1,p(x)}(\Omega )\overset{ (-\Delta _{p(x)})^{-1}}{\longrightarrow } W_{0}^{1,p(x)}(\Omega ) \) is strongly continuous. Let \( (\jmath _n)\subset D \) be a sequence such that converges weakly to \( \jmath _{0}\) in D . By the strong continuity of \( \overline{F},\) it follows that \( \overline{F}(\jmath _n)\longrightarrow \overline{F}(\jmath _0)\) and the strong convergence of \( T(\jmath _n)\longrightarrow T({{{\jmath }}}_0)\) is ensured by the continuity of \((-\Delta _{p(x)})^{-1}.\)

T is compact.

D is bounded. For \( \jmath \in D, \) we have \( \Arrowvert \jmath \Arrowvert \le \Arrowvert \vartheta \Arrowvert + \Arrowvert \nu \Arrowvert .\)

\( T(D) \subset D. \) Because, if \( \jmath \in D \) , then \( \vartheta (x)\le \jmath (x)\le \nu (x), \;x \in \Omega .\) Using assumptions \( A_3\) and \(A_4\) we have \( f(x,\vartheta (x))\le f(x, \jmath (x))\le f(x, \nu (x)).\) Therefore, for any \( v \in W_{0}^{1,p(x)}(\Omega ), \, v \ge 0\) we have

By the definition of \(\vartheta \) and \(\nu \) we can write

According to the maximum principle and the monotonicity of \( (-\Delta _{p(x)})^{-1},\) we have

which implies

By the Schauder’s fixed point Theorem 2.12 , T has a fixed point which is a solution for ( 1.1 ). \(\square \)

If in Theorems 3.1 and 3.2 , we assume that there exists \( x_0 \in \Omega \) with \( f(x_0, 0) \ne 0,\) then the solution of problem ( 1.1 ) is non trivial.

For the purpose of support, we provide an example that is completely consistent with the theoretical findings.

Example 3.4

Let \(X=\mathbb {R}^2\) , \(\Omega =\{(x_1,x_2):\frac{1}{9}<{x_1}^2+{x_2}^2<\frac{1}{4}\}\) . Define \( p:\overline{\Omega }\rightarrow \mathbb {R}\) , by

Therefore, we have

where \(\Omega _1^p=\{x\in \Omega :p(x)=1\}\) and \(\Omega _\infty ^p=\{x\in \Omega :p(x)=\infty \}\) , we can obtain; \(p^{\prime }(x:=(x_1,x_2))=1+\frac{{x_1}^2}{{x_2}^2}\) .

Consider the following p ( x )–Laplacian Dirichlet problem:

Setting \(\vartheta _1=1\) , \(\kappa =1\) and \( \vartheta _0\ge \frac{\Vert \jmath \Vert _{p(x)}}{\Vert \nabla \jmath \Vert _{p(x)}}, \) we obtain

Therefore, condition \(A_2\) of Theorem 3.1 is satisfied. Moreover, \(A_1\) of Theorem 3.1 holds. Hence, it is easy to see that f is a Carathéodory function and the conditions of Theorem 3.1 are satisfied. Therefore, we conclude that problem ( 3.3 ) admits at least a non–trivial solution in \(W_{0}^{1,p(x)}(\Omega ).\)

4 Conclusion

Despite its significance, the investigation of the existence of solutions for elliptic BVPs with the p ( x )-Laplacian equation has received limited attention from interested scholars who have elaborated on this topic using various methodologies.

In this paper, we present some different conditions that allow using of variational and topological methods in the case of p ( x )-Laplacian to prove the existence of solutions for elliptic BVPs with the p ( x )-Laplacian equation. Main theorems are proven using fixed point theorems and the sub-supersolution approach. The paper presents key discoveries on the variable exponent Sobolev space, as well as basic features of the p ( x )-Laplacian and Nemytskii operators. When compared to earlier findings, the assumptions made concerning the nonlinearity f in ( 1.1 ) appear to be less restrictive given its structure.

It should be emphasised that the findings of this study are significant since they provide a novel approach for establishing the primary results, which can be used to examine solutions for Kirchhoff’s non-local version of the p -Laplace equations in the future.

Abid, I., Baraket, S., Jaidane, R.: On a weighted elliptic equation of \(N\) -Kirchhoff type. Demonstr. Math. 55 , 634–657 (2022). https://doi.org/10.1515/dema-2022-0156

Article   MathSciNet   Google Scholar  

Agrawal, R.P., O’regan, D., Sahu, D.R.: Fixed Point Theory for Lipschitzian-Type Mappings with Application. Springer; (2009)

Agrawal, R.P., Meehan, M., O’regan, D.: Fixed Point Theory and Applications, Cambridge University Press; (2004)

Ahmad, M., Zada, A., Alzabut, J.: Stability analysis for a nonlinear coupled implicit switched singular fractional differential system with \(p\) -Laplacian. Adv. Differ. Equs. 436 , 1–22 (2019). https://doi.org/10.1186/s13662-019-2367-y

Cerami, G., Solimini, S., Struwe, M.: Some existence results for superlinear elliptic boundary value problems involving critical exponents. J. Funct. Anal. 69 , 289–306 (1986)

Chen, Y., Gao, H.: Existence of positive solutions for nonlocal and nonvariational elleptic systems. Bull. Aust. Math. Soc. 7 (2), 271–281 (2005)

Article   Google Scholar  

Ding, M.Y., Zhang, C., Zhou, S.L.: On optimal \(C^{1,\alpha }\) estimates for p(x)-Laplace type equations. Nonlinear Anal. 200 , 112030 (2020)

Fan, X., Zhao, D.: On the spaces \( L^{p(x)}(\Omega )\) and \(W^{m,p(x)}(\Omega ).\) . J. Math. Anal. Appl. 263 , 424–446 (2001)

Fan, X., Shen, J., Zhao, D.: Sobolev embedding theorems for spaces \( W^{k,p(x)}(\Omega ).\) . J. Math. Anal. Appl. 262 , 749–760 (2001)

Fan, X.: On the sub-supersolution method for \(p(x)\) -Laplacian equation. J. Math. Anal. Appl. 330 , 665–682 (2007)

Faria, L.F.O.: Existence and uniqueness of positive solutions for singular biharmonic elleptic systems. Dynamical Systems, Differential Equations and Applications AIMS Proceedings. (2015), pp. 400-408. https://doi.org/10.3934/proc.2015.0400

Hammou, M.A., Azroul, E., Lahmi, B.: Existence of solutions for \(p(x)\) -Laplacian Dirichlet problem by topological degree. Bull. Transilv. Univ. Bras. Ser. III (11), 29–38 (2018)

MathSciNet   Google Scholar  

Heidarkhani, S., Caristi, G., Ferrara, M.: Perturbed Kirchhoff-type Neumann problems in Orlicz-Sobolev spaces. Comput. Math. Appl. 71 (10), 2008–2019 (2016)

Heidarkhani, S., Ghobadi, A., Avci, M.: Multiple solutions for a class of \(p (x)\) -Kirchhoff-type equations. Appl. Math. E-Notes. 22 , 160–168 (2022)

Heidarkhani, S., Moradi, S., Barilla, D.: Existence results for second-order boundary-value problems with variable exponents. Nonlinear Anal. Ser. B: Real World Appl. 44 , 40–53 (2018)

Heidarkhani, S., Afrouzi, G.A., Moradi, S.: Variational approaches to \(p(x)\) -Laplacian-like problems with Neumann condition originated from a capillary phenomena. Int. J. Nonlinear Sci. Numer. Simul. 19 , 189–204 (2018)

Heidarkhani, S., De Araujo, A.L.A., Afrouzi, G.A., Moradi, S.: Multiple solutions for Kirchhoff type problems with variable exponent and nonhomogeneous Neumann conditions. Math. Nachrichten. 291 (2–3), 326–342 (2018)

Hsini, M., Irzi, N., Kefi, K.: Nonhomogeneous \(p\) -Laplacian Steklov problem with weights. Complex Var Elliptic Equs. 65 , 440–454 (2020). https://doi.org/10.1080/17476933.2019.1597070

Ilyas, P.S.: Dirichlet problem with \(p\) -Laplacian. Math. Rep. 10 (60), 43–56 (2008)

Khaleghi, A., Razani, A., Safari, F.: Three weak solutions for a class of p(x)-Kirchhoff type biharmonic problems. Lobachevskii J. Math. 44 (12), 5298–5305 (2023)

Khaleghi, A., Razani, A.: Solutions to a (p(x); q(x))-biharmonic elliptic problem on a bounded domain. Bound. Value Prob. 2023 , 53 (2023)

Khaleghi, A., Razani, A.: Existence and multiplicity of solutions for p(x)-Laplacian problem with Steklov boundary condition. Bound. Value Prob. 39 , 11 (2022)

Kefi, K.: \(p\) -Laplacian with indefinite weight. Proc. Am. Math. Soc. 139 (12), 4351–4360 (2011)

Le, V.K.: On a sub-supersolution method for variational inequalities with Leray-Lions operators in variable exponent spaces. Nonlinear Anal. 71 , 3305–3321 (2009)

Liao, F.-F., Heidarkhani, S., Moradi, S.: Multiple solutions for nonlocal elliptic problems driven by \(p(x)\) -biharmonic operator. AIMS Math. 6 (4), 4156–4172 (2021)

Mao, A., Zhu, Y., Luan, S.: Existence of solutions of elliptic boundaryvalue problems with mixed typenonlinearities. Bound. Value Prob. 97 (2012)

Mahshid, M., Razani, A.: A weak solution for a (p(x); q(x))-Laplacian elliptic problem with a singular term. Bound. Value Prob. 2021 , 80 (2021)

Moussaoui, M., Elbouyahyaoui, L.: Existence of solution for Dirichlet problem with \(p\) -Laplacian. Bull. Paranans Math. Soc. 33 (2), 243–250 (2015)

Nhan, L.C., Chuong, Q.V., Truong, L.X.: Potential well method for p(x)-Laplacian equations with variable exponent sources. Nonlinear Anal. Real World Appl. 56 , 103155 (2020)

Ok, J.: Harnack inequality for a class of functionals with non-standard growth via De Giorgi method. Adv. Nonlinear Anal. 7 , 167–182 (2018)

Orlicz, W.: Uber konjugierte Exponentenfolgen. Stud. Math. 3 , 200–212 (1931)

Precup, R.: Implicit elliptic equations via Krasnoselski-Schaefer type theorems. Electron. J. Qual. Theory Differ. Equs. 87 , 1–9 (2020). https://doi.org/10.14232/ejqtde.2020.1.87

Rajagopal, K.R., Ruzicka, M.: Mathematical modeling of electrorheological materials. Contin. Mech. Thermodyn. 13 , 59–78 (2001)

Razani, A., Costa, G.S., Figueiredo, G.M.: A positive solution for a weighted p-Laplace equation with Hardy-Sobolev’s critical exponent. Bull. Malay. Math. Sci. Soc. 47 , 61 (2024)

Razani, A.: Entire weak solutions for an anisotropic equation in the Heisenberg group. Proc. Am. Math. Soc. 151 (11), 4771–4779 (2023)

Ruzicka, M.: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics; Springer: Berlin, Germany, 1748 (2000)

Smart, D.R.: Fixed Point Theorems. Cambridge University Press (1974)

Sousa, J. V. D. C.: Fractional Kirchhoff-type systems via sub-supersolutions method in \(\mathbb{H}^{\alpha ,\beta ;\psi }_{p}(\Omega )\) . Rend. Circ. Mat. Palermo, II. Ser (2023). https://doi.org/10.1007/s12215-023-00942-z

Su, J.B., Zhao, L.: An elliptic resonance problem with multiple solutions. J. Math. Anal. Appl. 319 , 604–616 (2006)

Vetro, C.: Variable exponent \(p(x)\) -Kirchhoff type problem with convection. J. Math. Anal. Appl. 506 (2), 125721 (2022)

Wang, B.S., Hou, G.L., Ge, B.: Existence and uniqueness of solutions for the \(p(x)\) -Laplacian equation with convection term. Mathematics. 8 , 1768 (2020)

Xie, W.L., Chen, H.B.: Existence and multiplicity of solutions for \(p(x)\) -Laplacian equations in \(\mathbb{R} ^N\) . Math. Nachr. 291 , 2476–2488 (2018)

Yao, F.P.: Local Holder estimates for non-uniformly variable exponent elliptic equations in divergence form. Proc. R. Soc. Edinb. Sect. A. 148 , 211–224 (2018)

Zhao, D., Fan, X.L.: The Nemytski operators from \( L^{p_{1}(x)}(\Omega )\) to \( L^{p_{2}(x)}(\Omega ).\) . J. Lanzhou Univ. 34 (1), 1–5 (1998)

Zhang, Y., Feng, M.: A Coupled p-Laplacian elleptic system: existence, uniqueness and asymptotic behavior. Electron. Res. Archiv. 28 (4), 1419–1438 (2020). https://doi.org/10.3934/era.2020075

Zhikov, V.V.: Averaging of functionals of the calculus of variations and elasticity theory. Math USSR Izv. 9 , 33–66 (1987)

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J. Alzabut is thankful to Prince Sultan University and OSTİM Technical University for their endless support.

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Ayadi, S., Alzabut, J., Afshari, H. et al. Existence of Solutions for p ( x )-Laplacian Elliptic BVPs on a Variable Sobolev Space Via Fixed Point Theorems. Qual. Theory Dyn. Syst. 23 , 195 (2024). https://doi.org/10.1007/s12346-024-01054-4

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Chapter VII – Inventive step

Marcos adopts area-specific approach to El Niño

President Marcos is pushing for area-specific ways of addressing the problems created by the El Niño phenomenon especially in hardest-hit provinces where a state of calamity has been declared.

President Ferdinand 'Bongbong' Marcos jr. presides over a sectoral meeting in Malacañang. (Photo from the Presidential Communications Office)

The Chief Executive explained that the government is looking at the problems “by area” to come up with solutions to help the farmers and those impacted by the high temperatures.  

“Iba-iba ‘yung problema sa bawat lugar, eh. Hindi naman pwede shotgun lang parang one size fits all (There are different problems in each area. It cannot be a shotgun where one size fits all),” he told reporters in Bacolod City, where he led the opening of the Cebu-Negros-Panay 230-kV Backbone Project.  

“So we look at each area and see what it is that they need. So that's the way we are handling the local states of calamity that the local governments have declared,” he added.  

Earlier, Task Force El Niño spokesperson Joey Villarama said that 16 towns have already declared a state of calamity due to El Niño.  

While Marcos furthered that all provinces will be affected by El Niño, he admitted that some provinces would be in a more difficult state compared to others.  

The President also gave a rundown of what the government has been doing to counter its effects, adding that the government is looking particularly at areas that cannot be reached by water and irrigation.  

“As a matter of fact, kasi naglagay nga tayo ng mga dam, patuloy na inaayos ang ating irigasyon (we put up dam, we are fixing the irrigation), we should and we are trying to find new techniques of planting,” he said.  

“We are harvesting more palay now than we are last year, that's despite the El Niño, so it's taking effect,” he added.  

According to the Department of Agriculture (DA), the damage and losses incurred by the agriculture sector due to the El Niño phenomenon have reached P2.63 billion.  

This translates to 53,879 hectares of farmland that that have been affected, equivalent to 116,792 metric tons of production volume.