Multiplicity results for a three-point boundary value problem at resonance.
type: Item
instance of: scholarly article
title: Multiplicity results for a three-point boundary value problem at resonance.
zbMATH Open document ID: 1037.34011
DOI: 10.1016/S0362-546X(03)00033-6
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2003-05-14T00:00:00Z
review text: This paper deals with the three-point boundary value problem \[ u''=f(t,u) \quad \text{for}\;t\in(0,1), \quad u(0)=0,\;u(1)=\alpha u(\eta), \] where \(f:[0,1]\times \mathbb R\times \mathbb R\) is continuous, \(\alpha\in(0,\infty)\) and \(\eta\in(0,1)\) are given constants such that \(\alpha\eta=1\). We develop the method of lower and upper solutions by connectivity properties of the solution set of parameterized families of compact vector fields. As applications of these method, we get several multiplicity results for the problems under consideration.
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 1910237
zbMATH Keywords: multipoint boundary value problem
zbMATH Keywords: multiplicity
zbMATH Keywords: at resonace
zbMATH Keywords: connected sets
author: Ruyun Ma
reviewed by: Yujun Dong
MaRDI profile type: Publication
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full work available at URL: s0362-546x(03)00033-6
OpenAlex ID: W1972041601
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description: scientific article; zbMATH DE number 1910237