Article
Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations
Author/s | Caraballo Garrido, Tomás
Cheban, David |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2011 |
Deposit Date | 2015-04-08 |
Published in |
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Abstract | The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation
x′′ + f(x)x′ + g(x) = F(t),
where F : T ! R (T = R+ or R) is an almost periodic or ... The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation x′′ + f(x)x′ + g(x) = F(t), where F : T ! R (T = R+ or R) is an almost periodic or asymptotically almost periodic function and g : (a, b) ! R is a strictly decreasing function. We study also this problem for the vectorial Li´enard equation. We analyze this problem in the framework of general non-autonomous dynamical systems (cocycles). We apply the general results obtained in our early papers [3, 7] to prove the existence of almost periodic (almost automorphic, recurrent, pseudo recurrent) and asymptotically almost periodic (asymptotically almost automorphic, asymptotically recurrent, asymptotically pseudo recurrent) solutions of Li´enard equations (both scalar and vectorial). |
Citation | Caraballo Garrido, T. y Cheban, D. (2011). Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations. Discrete and Continuous Dynamical Systems. Series B, 16 (3), 703-717. |
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