Ulam Stability for a Class of Hill’s Equations

Round 1

Reviewer 1 Report

Solutions of Hill's equations are  found and the stability ( Ulam)of the solutions is given.

ADVANTAGES: 

The sufficient and necessary convergence criteria seem to be new.The proofs of the results are correct and well writtenThe results are broken down in small pieces,so the reader can follow easily. 

WEAKNESSES:

(1)ONCRETE REAL LIFE PROBLEMS SHOULD BE INSERTED WHERE THESE EQUATIONS CAN BU USED AND THE CRITERIA TESTED.

(2)Expand the abstract mentioning where these results find applications to increase readability.

(3)Insert a conclusion.

(4)Cite non-cited references or delete them.

(5)Compare these results with other using similar converence criteria or identical. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The title of the work corresponds to the content.

The paper has a first chapter in which a brief reference is made to the bibliography and it presents some useful theorems.

The second chapter presents a theorem proving the problem Ulm stability of nonhomogenous equations, starting from a first order equation.

In chapters 3 and 4 there are some theorems, some remarks and two examples, stating from a second order derivative equation.

The paper has no conclusions.

The bibliography is relatively recent.

The mathematical research method is at the level of the inhomogeneous differential equations, with a related analysis. Theorems on the analyzed problem are stated and proved.

The paper requires a deeper discussion of the problem.

The paper requires conclusions on the results, reaffirmation of contributions and prospects of application.

The work has consistency and it may be published after some revision using the above remarks.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

the article discuss about Ulam stability: the abstract could be considered well posed, but the introduction needs to be better explained: the context must better specified.

section 2 and 3 are well presented and contain exhaustive description of the results.

a final section with conclusions remarks and contents it is necessary.

finally, to better enlarge the context of the article in the introduction could be useful to add the following paper:

[1] Cesarano C, Bazighifan O (2019). Qualitative Behavior of Solutions of Second Order Differential Equations. SYMMETRY, vol. 11, p. 1-8, ISSN: 2073-8994, doi: https://doi.org/10.3390/sym11060777

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Paper is ok now.