Review Reports

Round 1

Reviewer 1 Report

Please see attached file

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In the paper under review, the authors obtain sufficient conditions for the existence of a bifurcation point for nonlinear periodic third-order differential equations. The proofs are based on Leray–Schauder’s topological degree theory. An illustrative example is given in the last section of the paper. The obtained results have some interest, but the authors did not substantiate the motivation for this study.

In particular, it is required to give examples of the application of the obtained results in mathematical modeling of real phenomena. It is not enough only general phrases such as ''Third-order equations, known in the literature as jerk equations, have been studied by many authors, not only from a purely mathematical approach but also in several fields where the study of the jerk dynamics is relevant'' (see Page 2). Is there a reason to study this? Is it a pure mathematical interest? What contribution do the results make to the relevant theory? What consequences will the results have? Mere formal correctness of a paper is not sufficient for its acceptance.

As usual, papers reporting a merely marginal extension of already existing knowledge are considered unsatisfactory.

Moreover, I noticed that the conclusion section is missing. It is a serious flaw.

Therefore, I ask the authors to address the above questions more carefully in order to provide more valuable work for the scientific community.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have revised and improved the quality of the manuscript by addressing my comments. I can recommend this paper for publication in Axioms provided that the authors will make a minor revision of the Conclusion section. Namely, this section should give a detailed explanation of the following questions.

(i) What contribution do the results make to the subject area?

(ii) What consequences will the results have?

(iii) What is the direction of future research?

Author Response

The Conclusion was rewritten according to the 2nd report of Reviewer 2