Positive solutions of second order systems of boundary value problems
type: Item
instance of: scholarly article
title: Positive solutions of second order systems of boundary value problems
zbMATH Open document ID: 0807.34024
author: A. M. Fink
author: Juan A. Gatica
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-03-01T00:00:00Z
review text: The authors consider the boundary value problem: \(x''(t)+ \lambda a(t)f(x(t),y(t))= 0\), \(y''(t)+ \lambda b(t)g(x(t),y(t))= 0\), \(x(0)= x(1)= y(0)= y(1)= 0\), where \(f\) and \(g\) are continuous vector functions, componentwise nonnegative and increasing in each variable, \(a\) and \(b\) are continuous and nonnegative diagonal matrices. In these assumptions, they determine a set of values of \(\lambda>0\) in order that the problem has a nonnegative solution \((x,y)\), proving that it is not trivial when \(f(0,0)= g(0,0)= 0\) and \(f\) and \(g\) are superlinear. The results apply, for instance, when \(f(x,y)= y^ p\), \(g(x,y)= x^ q\) \((p,q>1)\) or \(f(x,y)= e^ y\), \(g(x,y)= e^ x\). The method of proof is topological.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 562695
zbMATH Keywords: topological methods
zbMATH Keywords: boundary value problem
zbMATH Keywords: nonnegative solution
reviewed by: Gabriella Caristi
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1385
OpenAlex ID: W1981853421
DOI: 10.1006/JMAA.1993.1385
description: scientific article; zbMATH DE number 562695