Periodic solutions of linear, Riccati, and Abel dynamic equations

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 uppe...

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Detalles Bibliográficos
Autores: Bohner, Martin|||0000-0001-8310-0266, Gasull, Armengol|||0000-0002-1719-8231, Valls, Clàudia|||0000-0001-8279-1229
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:204401
Acceso en línea:https://ddd.uab.cat/record/204401
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2018.10.018
Access Level:acceso abierto
Palabra clave:Linear
Riccati and Abel differential and difference equations
Time scales
Periodic function
Melnikov function
Descripción
Sumario: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.