Positive solutions of nonlinear three-point boundary-value problems
type: Item
instance of: scholarly article
title: Positive solutions of nonlinear three-point boundary-value problems
zbMATH Open document ID: 1028.34014
DOI: 10.1016/S0022-247X(02)00661-3
author: Haiyan Wang
author: Ruyun Ma
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: The authors study the existence of positive solutions to the nonlinear three-point boundary value problem \[ u''(t)+a(t)u'(t)+b(t)u(t)+h(t)f(u)=0,\quad t\in (0,1),\quad u(0)=0,\quad \alpha u(\eta)=u(1), \] where \(0<\eta<1,\) \(f\in C([0,\infty),[0,\infty)),\) \(h\in C([0,1],[0,\infty))\) and there exists \(x_{0}\in [0,1]\) such that \(h(x_{0})>0,\) \(a\in C[0,1]\) and \(b\in C([0,1],(-\infty,0)).\) They prove the existence of at least one positive solution if \(f\) is either superlinear or sublinear by applying the fixed-point theorem in cones.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1915744
zbMATH Keywords: second-order multi-point boundary value problem
zbMATH Keywords: positive solution
zbMATH Keywords: cone
zbMATH Keywords: fixed-point
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1915744