Differential and Integral Equations

Structure of the set of bounded solutions and existence of pseudo almost-periodic solutions of a Liénard equation

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.

Article information

Source
Differential Integral Equations Volume 20, Number 7 (2007), 793-813.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356039410

Mathematical Reviews number (MathSciNet)
MR2333657

Zentralblatt MATH identifier
1212.34113

Subjects
Primary: 34C27: Almost and pseudo-almost periodic solutions
Secondary: 34C11: Growth, boundedness 34D05: Asymptotic properties

Citation

Ait Dads, El Hadi; Lhachimi, Lahcen; Cieutat, Philippe. Structure of the set of bounded solutions and existence of pseudo almost-periodic solutions of a Liénard equation. Differential Integral Equations 20 (2007), no. 7, 793--813.https://projecteuclid.org/euclid.die/1356039410