Positive solutions for a second-order differential system
type: Item
instance of: scholarly article
title: Positive solutions for a second-order differential system
zbMATH Open document ID: 1217.34036
author: Fanglei Wang
author: Yukun An
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-10-25T00:00:00Z
review text: The authors study the existence of positive solutions of the second-order system \[ \begin{gathered} -u''+\lambda u =\varphi u+f(t,u),\;t \in (0,1),\\ -\varphi''=\mu u,\;t \in (0,1),\\ u(0) =u(1) =0,\\ \varphi(0) =\varphi(1) =0,\\ \end{gathered} \] where \(\lambda > -\pi^2\), \(\mu\) is a positive parameter, and the nonlinearity \(f\) is allowed to be singular. The main tool used in this paper is Krasnosel'skiĭ's theorem on cone compression and cone expansion.
reviewed by: Gennaro Infante
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5804511
zbMATH Keywords: second-order system
zbMATH Keywords: positive solution
zbMATH Keywords: cone
zbMATH Keywords: fixed point
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.07.031
OpenAlex ID: W2083484464
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DOI: 10.1016/J.JMAA.2010.07.031
description: scientific article; zbMATH DE number 5804511