On the structure of the set of bounded solutions on an almost periodic Liénard equation
type: Item
instance of: scholarly article
title: On the structure of the set of bounded solutions on an almost periodic Liénard equation
zbMATH Open document ID: 1059.34030
author: P. Cieutat
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-01T00:00:00Z
review text: The Liénard equation \[ x''+f(x)x'+g(x)=p(t) \] is studied, where \(p:{\mathbb R}\rightarrow {\mathbb R}\) is continuous and \(f,g:(a,b)\rightarrow {\mathbb R}\) are locally Lipschitz. Additionally, \(p\) is an almost-periodic function, and \(g\) is strictly decreasing. A set of initial conditions of the bounded solutions on \((0,\infty )\) is described, and it is shown that these solutions are asymptotically almost-periodic. A model example of this equation is the equation \[ x''+cx'+(1/x^{\alpha})=p(t), \quad c\geq 0 \text{ and }\alpha >0, \] which has a singular nonlinear restoring force.
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 2105453
zbMATH Keywords: bounded solutions
zbMATH Keywords: asymptotic almost-periodic solutions
zbMATH Keywords: Liénard equation
MaRDI profile type: Publication
full work available at URL: j.na.2003.12.005
OpenAlex ID: W2031981486
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DOI: 10.1016/J.NA.2003.12.005
description: scientific article; zbMATH DE number 2105453