The existence of positive solutions for some nonlinear equation systems
type: Item
instance of: scholarly article
title: The existence of positive solutions for some nonlinear equation systems
zbMATH Open document ID: 1111.34021
author: Baofang Liu
author: Jihui Zhang
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: The authors consider the existence of positive solutions of the following boundary value problem: \[ \begin{cases} (\phi_1(x'))'+a(t)f(x,y)=0,&(\phi_2(y'))'+b(t)g(x,y)=0,\quad t\in(0,1),\\ \alpha\phi_1(x(0))-\beta\phi_1(x'(0))=0,&\alpha\phi_2(y(0))-\beta\phi_2(y'(0))=0,\\ \gamma\phi_1(x(1))+\mu\phi_1(x'(1))=0,&\gamma\phi_2(y(1))+\mu\phi_2(y'(1))=0, \end{cases} \] where \(\phi_1,\phi_2:\mathbb R\to\mathbb R\) are homeomorphisms and \(\phi_1(0)=0,\) \(\phi_2(0)=0\). They present sufficient conditions for the existence of positive solutions by using a fixed-point theorem.
reviewed by: Gennaro Infante
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5072998
zbMATH Keywords: boundary value problems
zbMATH Keywords: positive solution
zbMATH Keywords: cone
zbMATH Keywords: fixed-point
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.12.049
OpenAlex ID: W1983779000
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DOI: 10.1016/J.JMAA.2005.12.049
description: scientific article; zbMATH DE number 5072998