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2007 Structure of the set of bounded solutions and existence of pseudo almost-periodic solutions of a Liénard equation
El Hadi Ait Dads, Philippe Cieutat, Lahcen Lhachimi
Differential Integral Equations 20(7): 793-813 (2007).

Abstract

We study some of the properties of bounded, asymptotically almost-periodic or pseudo almost-periodic solutions of the Liénard equation, $$x'' + f(x)x' + g(x) = p(t) ,$$ where $p : \mathbb R \longrightarrow \mathbb R$ is a continuous, bounded, asymptotically almost-periodic or pseudo almost-periodic function, $f$ and $g : (a,b) \longrightarrow \mathbb R$ are continuous and $g$ is strictly decreasing. Notably, we describe the set of initial conditions of the bounded solutions on $( 0 , + \infty )$ and we state some results of existence of pseudo almost-periodic solutions.

Citation

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El Hadi Ait Dads. Philippe Cieutat. Lahcen Lhachimi. "Structure of the set of bounded solutions and existence of pseudo almost-periodic solutions of a Liénard equation." Differential Integral Equations 20 (7) 793 - 813, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.34113
MathSciNet: MR2333657

Subjects:
Primary: 34C27
Secondary: 34C11, 34D05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 7 • 2007
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