Existence and multiplicity of positive solutions for multi-parameter three-point differential equations system
type: Item
instance of: scholarly article
title: Existence and multiplicity of positive solutions for multi-parameter three-point differential equations system
zbMATH Open document ID: 1113.34017
author: Xian Xu
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-12-07T00:00:00Z
review text: The author studies, via fixed point index theory, the existence and multiplicity of positive solutions of a system of second order differential equations of the type \[ \begin{gathered} u''(t)+\lambda a_{1}(t) f_{1}(u(t),v(t))=0, \; t \in (0,1),\\ v''(t)+\mu a_{2}(t) f_{2}(u(t),v(t))=0, \; t \in (0,1),\\ \end{gathered} \] subject to the boundary conditions \[ \begin{gathered} u(0)=0,\;\; u(1)= \alpha_{1} u(\eta_{1}),\\ v(0)=0,\;\; v(1)= \alpha_{2} u(\eta_{2}).\\ \end{gathered} \] Here, \(\lambda\) and \(\mu\) are positive parameters, \(0 < \eta_{2} \leq \eta_{1}<1\), \(\alpha_{1}, \alpha_{2} \in (0,1),\) and \(a_{1}, a_{2}, f_{1}, f_{2}\) are continuous functions. The author of this paper remarks that, unlike what usually happens in previous results for systems, here the two nonlinearities possess a somewhat different behavior. In fact, the function \(a_{1}\) is positive and \(f_{1}\) is bounded below by a negative constant, whereas \(f_{2}\) is positive and the function \(a_{2}\) is allowed to change sign.
reviewed by: Gennaro Infante
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5078076
zbMATH Keywords: semi-positone problem
zbMATH Keywords: three-point boundary value problem
zbMATH Keywords: system
zbMATH Keywords: fixed point index
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.12.026
OpenAlex ID: W2038901169
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DOI: 10.1016/J.JMAA.2005.12.026
description: scientific article; zbMATH DE number 5078076