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| Pàgina inicial > Articles > Articles publicats > Higher order averaging theory for finding periodic solutions via Brouwer degree |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)| Data: | 2014 |
| Resum: | 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. |
| Ajuts: | Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338 |
| Nota: | Agraïments: The second author is partially suported by the grant FAPESP 2011/03896-0. The third author is partially supported by a FAPESP-BRAZIL grant 2007/06896-5. The first and third authors are also supported by the joint project CAPES-MECD grant PHB-2009-0025-PC. |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Matèria: | Averaging theory ; Brower degree ; Periodic solutions |
| Publicat a: | Nonlinearity, Vol. 27 (2014) , p. 563-583, ISSN 1361-6544 |
15 p, 424.0 KB |
