Title

Periodic Solutions of Linear, Riccati, and Abel Dynamic Equations

Abstract

We study the number of periodic solutions of linear, Riccati and Abel dynamic equations in the time scales setting. In this way, we recover known results for corresponding differential equations and obtain new results for associated difference equations. In particular, we prove that there is no upper bound for the number of isolated periodic solutions of Abel difference equations. One of the main tools introduced to get our results is a suitable Melnikov function. This is the first time that Melnikov functions are used for dynamic equations on time scales.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Linear, Riccati and Abel differential and difference equations; Melnikov function; Periodic function; Time scales

International Standard Serial Number (ISSN)

0022-247X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Academic Press Inc., All rights reserved.

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