Higher order averaging theory for finding periodic solutions via Brouwer degree
In this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (-ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small p...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150723 |
| Acceso en línea: | https://ddd.uab.cat/record/150723 https://dx.doi.org/urn:doi:10.1088/0951-7715/27/3/563 |
| Access Level: | acceso abierto |
| Palabra clave: | Averaging theory Brower degree Periodic solutions |
| Sumario: | In this paper we deal with nonlinear differential systems of the form x'(t) = Xki=0εiFi(t, x) + εk+1R(t, x, ε), where Fi : R × D → Rn for i = 0, 1, · · · , k, and R : R × D × (-ε0, ε0) → Rn are continuous functions, T-periodic in the first variable, being D an open subset of Rn, and ε a small parameter. For such differential systems, which do not need to be of class C1, under convenient assumptions we extend the averaging theory for computing their periodic solutions to k-th order in ε. Some applications are also performed. |
|---|