Multi-point boundary value problems of second-order differential equations. I
type: Item
instance of: scholarly article
title: Multi-point boundary value problems of second-order differential equations. I
zbMATH Open document ID: 1066.34012
author: Lingju Kong
author: Qingkai Kong
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-10-01T00:00:00Z
review text: The authors study boundary value problem of second-order nonlinear differential equations with nonhomogeneous multipoint boundary conditions of the form \[ x''+f(t,x,x')=0,\quad t\in (0,1),\tag{\(*\)} \] \[ u'(0)-\sum_{i=1}^m a_iu'(t_i)=\lambda_1,\qquad u(1)-\sum_{i=1}^m b_iu(t_i)=\lambda_2. \tag{\(**\)} \] Results concerning the existence of solutions of \((*)\) and \((**)\) are established using the method of lower and upper solutions. Explicit ranges of values of \(\lambda_1\) and \(\lambda_2\) are determined for the existence of no solution, one solution and a positive solution. The plane of \(\lambda_1\) and \(\lambda_2\) is divided by a continuous curve \(\Gamma\) into two disjoint connected regions \(\Lambda_E\) and \(\Lambda_N\) such that the problem \((*)\) and \((**)\) has a solution for each \((\lambda_1,\lambda_2)\in \Lambda_E\) and has no solution for each \((\lambda_1,\lambda_2)\in \Lambda_N\). Examples are given to generate motivation.
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 2105455
zbMATH Keywords: existence and nonexistence of solutions
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: multipoint boundary value problem
zbMATH Keywords: nonlinear second-order equations
MaRDI profile type: Publication
full work available at URL: j.na.2004.03.033
OpenAlex ID: W2058862623
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DOI: 10.1016/J.NA.2004.03.033
description: scientific article; zbMATH DE number 2105455