Periodic solutions of Lienard differential equations via averaging theory of order two
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Teixeira, Marco Antonio (Universidade Estadual de Campinas(Brazil). Departamento de Matemática)

Date:	2015
Abstract:	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.
Grants:	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
Note:	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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Averaging theory ; Bifurcation theory ; Lienard differential equation ; Periodic solution
Published in:	Anais da Academia Brasileira de Ciencias, Vol. 87 Núm. 4 (2015) , p. 1905-1913, ISSN 1678-2690

DOI: 10.1590/0001-3765201520140129

Postprint 10 p, 300.3 KB

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