Solutions for Some Specific Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 2

Round 1

Reviewer 1 Report

Please see attached file for comments and suggestions.

Comments for author File: Comments.pdf

Author Response

Thank you for the careful reading and corrections made on my manuscript.  Please, find the answer attached below.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper under review is a direct follow-up for previously published paper  https://doi.org/10.3390/axioms12060532.

The Author reports some interesting applications for previously obtained theoretical results. My general concern is the high dependence of the current manuscript to the previous one. Despite follow-up papers are commonly acceptable practice, some minimal theoretical explanations should be given for the Reader to increase the understandability of current research.

My second concern is the structure of the paper - a lot of short and laconic sections and subsections make paper barely readable. I recommend restructurizing the manuscript bringing together theoretical results with their possible applications. 

E.g., I recommend expanding section 2 with a brief motivation. Subsection 2.1 title seems fragmentary. Again, minimal explanations should be given to avoid confusing the reader.

The formulae in the manuscript are not properly numbered, which complicates the referencing process.

The title of the paper is also too general for considered specific mathematical problems.

Section 5 - please, give further explanation to Proposition 10 and 11. Due to minimal difference between them, I believe they can be generalized as one.

In general, I believe the theory can be modified to be more elegant and less reduntant throughout the paper.

Minor issues: I recommend proofreading the paper to reduce the number of typos and grammar mistakes, e.g. "apply now Propositions 1, 2, 3, 4 in solving" - possibly, apply to solving will sound better. 

Please, also briefly clarify the contribution of the current paper after the following ones:

https://doi.org/10.1515/dema-2022-0024

Despite the abovementioned issues, I found the paper mathematically correct and therefore believe that it can be accepted for publication after major revisions.

The quality of English language, including both grammar and style issues, is to be significantly improved

Author Response

Thank you for the careful reading and corrections made on my manuscript.  Please, find the answer attached below.

Author Response File: Author Response.pdf

Reviewer 3 Report

I apologize with the author of this manuscript, but I am not able to understand the meaning and the usefulness of this work. Reading the abstract, one expects to find some new and interesting applications (i.e., numerical applications) of abstract results collected in a previous paper co-authored by the author of the paper under review. Now, reading the manuscript the above situation does not occur. Hence, the author presents in a fast way some specific settings of general nonlinear boundary value problems referring to the modeling process of certain physical situations, referring to a very partial bibliography on the main topic, and without providing more details and information to the readers. To be honest, the p-Laplacian type operators are well-motivated by the pioneering works of V.V. Zhikov and P. Marcellini, for their usefulness in modeling problems of fluid dynamics, elasticity theory homogenization problems. Summing up, I don't see strong motivations to recommend the publication of this manuscript.

Author Response

Please, find the answer attached below.

Author Response File: Author Response.pdf

Reviewer 4 Report

The main result of the author is an study of some problems of mathematical physics equations involving p-Laplacian and p-pseudo-Laplacian. The content of the article is fully theoretical and has an perspective to be applied to some practical applications. Thus, I can state that the paper fully relevant to the aims and scopes of the Journal ``Axioms'' (especially to the Section ``Mathematical Physics'').

The manuscript contains the statement of the problem and the methods for its solution, which are presented clearly. The motivation of the work and the contribution of the author to the topic are indicated. The article is well structured and written in a clear and concise manner. All of the references are appropriate.

I have only one minor remark. The title of the article is too general and may mislead a potential reader. The title of the article should fully correspond to the specific problem considered by the author in the article. Thus, I recommend specifying the title of the article.

Author Response

Thank you for the appreciation, the careful reading and suggestions made on my manuscript. Please, find the answer attached below.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Thank you very much for providing a revised version of the manuscript. I generally satisfied with the reply letter and the revisions provided. Besides, I still believe that manuscript will benefit from some further restructurization. In present form it looks more like textbook than scientific article. I also think that the given modification of the title adds nothing but bulkiness to it.

Nevertheless, I highly value the mathematical contribution of this study and I am sure that there is no need in second round of peer-review. I will recommend this paper to be accepted for publication in Axioms after minor revisions.

The English language and style need to be improved prior to publication.

Author Response

Dear reviewer, please find the answer attached below.

Author Response File: Author Response.pdf

Reviewer 3 Report

The only change realized by the authors in this revision is to add 19 references, without properly discussing their content and relevance to the the design of the study. As a consequence my concerns remain unsolved. Unfortunately, I cannot support the manuscript.

Author Response

Please, find the answer attached below.

Author Response File: Author Response.pdf

Round 3

Reviewer 3 Report

Surely this reviewer and the author of the manuscript under review have a different opinion about the relevance of the manuscript.  Clearly these opinions are also subjective opinions, but these are based on own knowledge of the topic and mathematical background, etc. Hence, I DO NOT think that my opinion is more valuable than that of the author, but I am free to support my arguments and follow my ideas. Consequently I disagree when the author concludes the cover-letter saying that "differences of opinion are not a reason for rejection.". Indeed, in my opinion the results in this paper does not provide any advantages/improvements to the level of knowledge on the topic, hence I don't consider that the paper deserves to be published in current form and without significant revision. For example, the short section 6.2 titled "Applications" does not contains any applications. In my opinion this section is just a remark. Last but not least, adding sentence as "A lot of methods use critical points theory to find or characterize solutions for (fractional) boundary problems...." is a trivial fact, known to every student of mathematics.