\(p\)-Laplacian and Liénard-type equation
type: Item
instance of: scholarly article
title: \(p\)-Laplacian and Liénard-type equation
zbMATH Open document ID: 0898.34021
author: Stanisław Sȩdziwy
author: Raúl Manásevich
published in: Rocky Mountain Journal of Mathematics
publication date: 1998-10-15T00:00:00Z
full work available at URL: CONT27-2.html
review text: Consider the Liénard-type equation \((*)\) \((|u'|^{p-2}u')' + \mu f(u)|u'|^{p-2}u' + g(u)=0\) where \(p>1\) and \(\mu\) is a small parameter. Under the assumptions that \(f\) and \(g\) are continuous and satisfy \(g(x)=-g(-x)\), \(g(x)x>0\) for \(x \neq 0\), \(f(x)=f(-x)\), and under additional conditions on \(F(x)=\int^x_0 f(s)ds\), the authors prove that \((*)\) has a unique limit cycle.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 1130576
zbMATH Keywords: Liénard-type equation
zbMATH Keywords: unique limit cycle
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
OpenAlex ID: W2077736556
cites work: Q5330830
cites work: Existence theorems for second order boundary value problems
cites work: Note on a nonlinear eigenvalue problem
cites work: A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
DOI: 10.1216/RMJM/1181071928
description: scientific article; zbMATH DE number 1130576