Home > Articles > Published articles > Periodic solutions of linear, Riccati, and Abel dynamic equations |
Date: | 2019 |
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. |
Grants: | Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Linear ; Riccati and Abel differential and difference equations ; Time scales ; Periodic function ; Melnikov function |
Published in: | Journal of mathematical analysis and applications, Vol. 470, Núm. 2 (February 2019) , p. 733-749, ISSN 1096-0813 |
Postprint 17 p, 389.6 KB |