Periodic solutions of Lienard differential equations via averaging theory of order two

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 f...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Novaes, Douglas D.|||0000-0002-9147-8442, Teixeira, Marco Antonio|||0000-0002-5386-9282
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:169442
Acceso en línea:https://ddd.uab.cat/record/169442
https://dx.doi.org/urn:doi:10.1590/0001-3765201520140129
Access Level:acceso abierto
Palabra clave:Averaging theory
Bifurcation theory
Lienard differential equation
Periodic solution
Descripción
Sumario: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.