Bounded solutions of nonlinear second order ordinary differential equations
type: Item
instance of: scholarly article
title: Bounded solutions of nonlinear second order ordinary differential equations
zbMATH Open document ID: 0954.34027
author: Alessandro Fonda
author: Fabio Zanolin
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The authors deal with the existence of bounded solutions on the whole real line to the forced Liénard equation \[ x''+f(x)x'+g(x)=e(t). \tag{1} \] Generalizations of recent results due to \textit{S. Ahmad} [Trans. Am. Math. Soc. 323, No.~2, 857-875 (1991; Zbl 0719.34062)] and \textit{R. Ortega} [Differ. Integral Equ. 8, No.~4, 729-734 (1995; Zbl 0817.34017)] are obtained. In case of a periodic forcing term, the established results allow to prove the existence of periodic solutions to (1).
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1492519
zbMATH Keywords: bounded solutions
zbMATH Keywords: nonlinear second-order forced differential equation
zbMATH Keywords: Landesman-Lazer type condition
zbMATH Keywords: Liénard equation
reviewed by: Svitlana P. Rogovchenko
MaRDI profile type: Publication
full work available at URL: dcds.1998.4.91
OpenAlex ID: W1983936609
DOI: 10.3934/DCDS.1998.4.91
description: scientific article; zbMATH DE number 1492519