Third-Order Nonlinear Semi-Canonical Functional Differential Equations: Oscillation via New Canonical Transform

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper the authors studied  the oscillatory properties of the semi-canonical nonlinear delay differential equation of third-order and the transformed the studied equation  into a canonical type equation and then we find the conditions for the oscillation of the studied equation from the canonical equations. The obtained results are new and complement to the existing results mentioned in the literature. Examples are provided to illustrate the importance and novelty of the main results.

However, I cannot give a recommendation for acceptance for the following reasons:

1- The paper is written in a random and poor manner. For example, the introduction is simple and does not clearly contain previous studies.

2- Theories are unclear and repetitive.

The paper needs more effort and better writing.

Author Response

The reviewer recommends for complete revision. Now the following changes are made

1. Abstract modified
2. Introduction part now modified and gives previous work and the motivation for the present work.
3. Examples provided to show the novelty of the main results.

4.Conclusion part also modified and suggestion   given for further work.

Reviewer 2 Report

Comments and Suggestions for Authors

The work is interesting and has good results. It is also written very carefully. I have very few comments:

1. if the work is typeset using LaTeX, then I suggest replacing the ":" sign (in places such as line 41 - in sup) with the "\colon" sign

2. above line 108 there is no comma between formulas

3. above line 179 the brackets in logarithms seem unnecessary

4. the literature does not appear in the right order

5. the literature is in the wrong format

6. it is necessary to present more (preferably at the beginning of the work) real and specific applications where the results achieved in the work have important applications - the authors mention this, but it seems that it is worth encouraging the reader by indicating more specific examples of applications

Author Response

 The Reviewer  comments and Answer:

1. if the work is typeset using LaTeX, then I suggest replacing the ":" sign (in places such as line 41 - in sup) with the "\colon" sign: Now corrected
2. above line 108 there is no comma between formulas: Now corrected
3. above line 179 the brackets in logarithms seem unnecessary: Brackets are removed
4. the literature does not appear in the right order: Now modified and arranged in order
5. the literature is in the wrong format: Modified and corrected
6. it is necessary to present more (preferably at the beginning of the work) real and specific applications where the results achieved in the work have important applications - the authors mention this, but it seems that it is worth encouraging the reader by indicating more specific examples:

Now a specific applications of our results presented  in the introduction part.

Reviewer 3 Report

Comments and Suggestions for Authors

See an attached file

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Trench proved in [24] that there exists only one canonical representation...

Let (2.1) holds

Set the right hand side of the last inequality

Application of Theorem 2.1.1 of [9] with (2.7) and (2.8) imply

Assume that there exists a function

Author Response

Recommended few suggestions:

1. Now the Abstract modified and simplified.

2.Yes, we use it

3. Now a brief summary of the content in the reference [20,21] given.
4. Introduction part now revised and modified .
5. Conclusion part modified and a suggestion for further direction is given.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The paper is now ready for publication but references should be reviewed and updated if possible.

Author Response

Comment: The paper is now ready for publication but references should be reviewed and updated if possible. Response : References are once again reviewed and it is already updated.

Reviewer 3 Report

Comments and Suggestions for Authors

There is a big formulae in the abstact.

I would also recommend using mdpi template.

The same comment about the cinclusion as in previous report.

 

Comments on the Quality of English Language

Let (2.1) holds - let (2.1) hold ? (in many sentences)

Application of Theorem 2.1.1 of [6] with (2.7) and (2.8) imply - application implies?

 

Author Response

1. Abstract modified without using big formula.
2. Paper changed in MDPI template.

3.Conclusion part modified and enlarged.

4.English language now edited and corrected.