Existence of three solutions for a nonautonomous two point boundary value problem
type: Item
instance of: scholarly article
title: Existence of three solutions for a nonautonomous two point boundary value problem
zbMATH Open document ID: 0980.34015
author: P. Candito
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-05-20T00:00:00Z
review text: Here, the author considers the two-point boundary value problem \[ u''+\lambda f(t,u)= 0,\quad u(a)= u(b)= 0,\tag{1} \] where \(f:[a, b]\times \mathbb{R}\to \mathbb{R}\) is a continuous function. Under some assumptions with respect to \(f(t,u)\) there exist an open interval \(\Lambda\subseteq ]0,+\infty[\) and a positive real number \(q\) such that, for each \(\lambda\in\Lambda\), the problem (1) admits at least three solutions belonging to \(C^2([a, b])\), whose norms in \(W^{1,2}_0([a, b])\) are less than \(q\).
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 1563078
zbMATH Keywords: nonlinear eigenvalue problem
zbMATH Keywords: Sobolev space
zbMATH Keywords: two-point boundary value problem
zbMATH Keywords: solutions
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6909
OpenAlex ID: W1969287479
cites work: Existence of three solutions for a two point boundary value problem
cites work: On a minimax problem of Ricceri
cites work: A new method for the study of nonlinear eigenvalue problems
cites work: On a three critical points theorem
cites work: Existence of three solutions for a class of elliptic eigenvalue problems
DOI: 10.1006/JMAA.2000.6909
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description: scientific article; zbMATH DE number 1563078