On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales-Reference-Cited by-同舟云学术

On the correspondence between periodic solutions of differential and dynamic equations on periodic time scales

Published:2024-02-09 Issue: Volume: Page:
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Tsan Viktoriia¹^ORCID,Stanzhytskyi Oleksandr¹^ORCID,Martynyuk Olha²^ORCID

Affiliation:

1. Faculty of Mechanics and Mathematics , Taras Shevchenko National University of Kyiv , Kyiv , Ukraine

2. Faculty of Mathematics and Informatics , Chernivtsi National University , Chernivtsi , Ukraine

Abstract

Abstract This paper studies the relationship between the existence of periodic solutions of systems of dynamic equations on time scales and their corresponding systems of differential equations. We have established that, for a sufficiently small graininess function, if a dynamic equation on a time scale has an asymptotically stable periodic solution, then the corresponding differential equation will also have a periodic solution. A converse result has also been obtained, where the existence of a periodic solution of a differential equation implies the existence of a corresponding solution on time scales, provided that the graininess function is sufficiently small.

Funder

National Research Foundation of Ukraine

Government of Ukraine

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2024-2003/pdf

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