Nonexistence and existence of multiple positive solutions for superlinear three-point boundary value problems via index theory
type: Item
instance of: scholarly article
title: Nonexistence and existence of multiple positive solutions for superlinear three-point boundary value problems via index theory
zbMATH Open document ID: 1168.34016
author: Baoqiang Yan
author: Donal O'Regan
author: Ravi P. Agarwal
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2008-10-27T00:00:00Z
review text: The paper is devoted to the three point boundary value problem \[ x''+ f(t,x,x')=0, \quad t\in (0,1), \] \[ x'(0)=0, \qquad x(1)=\alpha x(\eta), \] where \(f\) is nonnegative and continuous, \(\eta\in (0,1)\) and \(0<\alpha\eta<1\). Nonexistence of positive solutions is proved when \(f\) is superlinear in \(x'\) at \(0\). On the other hand, if \(f\) is superlinear in \(x'\) at \(\infty\), then, using topological fixed point index in an appropriate cone, the authors prove the existence of at least two positive solutions.
reviewed by: Pablo Amster
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5357860
zbMATH Keywords: three-point boundary value problems
zbMATH Keywords: fixed point index
MaRDI profile type: Publication
full work available at URL: s10255-007-7024-7
OpenAlex ID: W1996473234
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DOI: 10.1007/S10255-007-7024-7
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description: scientific article; zbMATH DE number 5357860