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...
| Autores: | , , |
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| 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 |
| 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. |
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