Positive periodic solutions to a nonlinear fourth-order differential equation
type: Item
instance of: scholarly article
title: Positive periodic solutions to a nonlinear fourth-order differential equation
zbMATH Open document ID: 1168.34033
author: Chunhua Jin
author: Jingxue Yin
author: Zejia Wang
published in: Communications on Pure and Applied Analysis
publication date: 2008-08-22T00:00:00Z
review text: The authors prove the existence of positive periodic solutions to a fourth-order differential equation of the type \[ u''''(t)+a(t)u(t)=f(t,u(t)). \] Denoting by \(T\) the period, it is assumed that \(0 \leq a(t) \leq 4(\pi/T)^4\), and a further condition is assumed on the asymptotic behaviour of \(f\) at \(0\) and at \(\infty\). Roughly speaking, the function \(f\) ``jumps'' the first eigenvalue of the associated linear equation. The proof uses the fixed point index theory in a cone.
reviewed by: Alessandro Fonda
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5315153
zbMATH Keywords: positive periodic solutions
zbMATH Keywords: the first positive eigenvalue
zbMATH Keywords: fixed point index
MaRDI profile type: Publication
full work available at URL: cpaa.2008.7.1225
OpenAlex ID: W2047586787
DOI: 10.3934/CPAA.2008.7.1225
description: scientific article; zbMATH DE number 5315153