Periodic solutions of linear, Riccati, and Abel dynamic equations
Bohner, Martin (Missouri S&T)
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Departamento de Matemática)

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
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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

DOI: 10.1016/j.jmaa.2018.10.018

Postprint 17 p, 389.6 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles