A priori bounds for periodic solutions of a Duffing equation
type: Item
instance of: scholarly article
title: A priori bounds for periodic solutions of a Duffing equation
zbMATH Open document ID: 1162.34031
author: Xinmin Wu
author: Yong Zhou
author: Jingwen Li
published in: Journal of Applied Mathematics and Computing
publication date: 2008-10-21T00:00:00Z
review text: Consider the scalar differential equation \[ x''+ cx'+ g(x)= p(t),\quad t\in\mathbb{R},\tag{\(*\)} \] where \(p\) is continuous, \(2\pi\)-periodic and with zero mean. By establishing a priori bounds for \(2\pi\)-periodic solutions of the auxiliary equation \[ x''+\lambda cx'+\lambda g(x)=\lambda p(t),\quad t\in\mathbb{R},\;\lambda\in (0,1) \] the authors prove under relatively simple conditions on \(c\), \(g\), \(p\) the existence of \(2\pi\)-periodic solutions of \((*)\) by using the coincidence degree.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5354619
zbMATH Keywords: Duffing equation
zbMATH Keywords: periodic solution
zbMATH Keywords: coincidence degree theorem
zbMATH Keywords: Liapunov function
MaRDI profile type: Publication
full work available at URL: s12190-007-0024-1
OpenAlex ID: W2036525793
cites work: Q4111886
cites work: Q3658347
cites work: A priori bounds for periodic solutions of a delay Rayleigh equation
cites work: Periodic solutions to Duffing equations with delay
cites work: Coincidence degree, and nonlinear differential equations
DOI: 10.1007/S12190-007-0024-1
description: scientific article; zbMATH DE number 5354619