## Differential and Integral Equations

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

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

El Hadi Ait Dads, Philippe Cieutat, and Lahcen Lhachimi

#### 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

**Permanent link to this document**

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