Resonance and nonresonance in terms of average values
type: Item
instance of: scholarly article
title: Resonance and nonresonance in terms of average values
zbMATH Open document ID: 0864.34015
author: Yanyan Li
published in: Journal of Differential Equations
publication date: 1997-06-23T00:00:00Z
review text: The problem \(u''(t)+k^2u(t)+g(u(x))+h(x)=0\), \(x\in(0,\pi)\), \(u(0)=x(\pi)=0\) is considered where \(k\) is a positive integer, \(g:\mathbb{R}\to\mathbb{R}\) is a continuous function with at most linear growth, and \(h\in L^2[0,\pi]\). Existence results are proved. The proofs rely on the Leray-Schauder degree argument and apply proved convergence results. Three illustrative examples are considered.
reviewed by: Josef Diblík
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 952549
zbMATH Keywords: two point nonlinear
zbMATH Keywords: boundary value problem
zbMATH Keywords: average values of the nonlinearities
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0170
OpenAlex ID: W2047036076
DOI: 10.1006/JDEQ.1996.0170
description: scientific article; zbMATH DE number 952549