Third-Order Noncanonical Neutral Delay Differential Equations: Nonexistence of Kneser Solutions via Myshkis Type Criteria

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

 

I hope this message finds you well. I have had the opportunity to review your manuscript on the oscillatory and asymptotic behaviors of third-order neutral delay differential equations, and I would like to commend you on your detailed mathematical analysis and contributions to the field.

 

Major Comments:

1. Assumptions Validation: It would enhance the paper if there were a more detailed justification for the assumptions (H1) - (H4). Discussing the typical conditions or models where these assumptions apply could clarify their relevance and limitations.

   

2. Operator Definitions:The paper would benefit from additional details on the conditions ensuring the existence and continuity of derivatives involved in operators \(L_1\), \(L_2\), and \(L_3\). Clarifying these conditions can help solidify the foundational mathematics of your analysis.

 

3. Transformation Justification:More rigorous explanations are needed for the transition of equation (E) into its canonical form, especially concerning the preservation of solution properties. This would strengthen the theoretical basis of your transformations and results.

 

Minor Comments:

1. Clarification of Notations:Some notations and function compositions (e.g., \(\tau \circ \delta\)) could be better defined for enhanced clarity and accessibility to readers less familiar with the field.

 

2. Literature Integration: A summary or table outlining how the cited literature supports your analysis could provide clearer context and highlight your manuscript’s novel contributions more explicitly.

 

3. Typographical Errors: A review for typographical and mathematical expression clarity could help in preventing potential misinterpretations and improve the professional presentation of your work.

 

Thank you for considering this feedback. I believe these enhancements will further strengthen your manuscript and its contribution to the understanding of differential equations.

 

Best regards,

Author Response

Please refer to the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Please check the attachment!

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Please check the attachment!

Author Response

Please refer to the attachment.

Author Response File: Author Response.pdf