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| Pàgina inicial > Articles > Articles publicats > Periodic solutions of Lienard differential equations via averaging theory of order two |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)| Data: | 2015 |
| Resum: | For ε = 0 sufficiently small we provide sufficient conditions for the existence of periodic solutions for the Lienard differential equations of the form x + f(x)x + n2x + g(x) = ε2p1(t) + ε3p2(t), where n is a positive integer, f : R → R is a C3 function, g : R → R is a C4 function, and pi : R → R for i = 1, 2 are continuous 2π-periodic function. The main tool used in this paper is the averaging theory of second order. We also provide one application of the main result obtained. |
| Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 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 supported by a FAPESP-BRAZIL grant 2012/10231-7. 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 ; Bifurcation theory ; Lienard differential equation ; Periodic solution |
| Publicat a: | Anais da Academia Brasileira de Ciencias, Vol. 87 Núm. 4 (2015) , p. 1905-1913, ISSN 1678-2690 |
10 p, 300.3 KB |
