A multiplicity result for a nonlinear boundary value problem
type: Item
instance of: scholarly article
title: A multiplicity result for a nonlinear boundary value problem
zbMATH Open document ID: 0899.34016
author: Kim Goudreau
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-09-09T00:00:00Z
review text: The paper contains some existence and multiplicity results of Ambrosetti-Prodi type on nonlinear boundary value problems the \[ x''(t)+x(t)+f(t,x(t),x'(t))=s\varphi (t), \quad t \in [0,\pi], \;x(0)=x(\pi)=\gamma, \] where \(f\) (a Carathéodory function) satisfies a condition which includes Bernstein-Nagumo and Wintner growth conditions, \(s\) and \(\gamma\) are real constants and \(\varphi\) is the principal positive eigenfunction of the corresponding homogeneous linear problem. In the proofs, the author uses lower and upper solutions and Leray-Schauder degree theory.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 1130506
zbMATH Keywords: nonlinear boundary value problems
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: resonance
zbMATH Keywords: existence
zbMATH Keywords: multiplicity
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: Leray-Schauder degree
reviewed by: Antonio Cañada
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5799
OpenAlex ID: W1974485098
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DOI: 10.1006/JMAA.1997.5799
description: scientific article; zbMATH DE number 1130506