Positive solutions for three-point boundary value problems with dependence on the first order derivative.
type: Item
instance of: scholarly article
title: Positive solutions for three-point boundary value problems with dependence on the first order derivative.
zbMATH Open document ID: 1054.34025
author: Yanping Guo
author: Weigao Ge
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-03-14T00:00:00Z
review text: The existence of positive solutions for the second-order three-point boundary value problem \(x''+f(t,x,x')=0\), \(0<t<1\), \(x(0)=0\), \(x(1)=\alpha x(\eta)\), is considered. It is supposed that \(\alpha>0\), \(0<\eta<1\), \(1-\alpha\eta>0\), and \(f:[0,1]\times [0,\infty)\times \mathbb R\to[0,\infty]\) is continuous. Under some growth conditions, the authors prove that the problem has at least one positive solution. As a tool for the proof a new fixed-point theorem in a cone is used.
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 2055379
zbMATH Keywords: three-point boundary value problem
zbMATH Keywords: fixed-point theorem in a cone
zbMATH Keywords: Green's function
zbMATH Keywords: positive solution
reviewed by: Josef Diblík
MaRDI profile type: Publication
full work available at URL: j.jmaa.2003.09.061
OpenAlex ID: W2005040284
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DOI: 10.1016/J.JMAA.2003.09.061
description: scientific article; zbMATH DE number 2055379