Periodic solutions of linear, Riccati, and Abel dynamic equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:470

Article

Bohner, Martin¹  Gasull, Armengol²  Valls, Claudia³ 

[1] Missouri S&T, Dept Math, Rolla, MO 65409 USA

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[3] Univ Lisbon, Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

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

DOI  :  10.1016/j.jmaa.2018.10.018

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free