Multiple positive solutions of Sturm-Liouville equations with singularities
type: Item
instance of: scholarly article
title: Multiple positive solutions of Sturm-Liouville equations with singularities
zbMATH Open document ID: 1123.34019
DOI: 10.1155/DDNS/2006/32018
author: Zenggui Wang
author: Lishan Liu
author: Yonghong Wu
published in: Discrete Dynamics in Nature and Society
publication date: 2007-03-19T00:00:00Z
full work available at URL: https://eudml.org/doc/128093
review text: The authors consider the second order Sturm-Liouville equation \[ (p(t) u'(t))' + g(t) F(t,u) = 0, \quad t \in (0, 1) \] with the (singular) boundary conditions \[ \alpha u(0) - \beta \lim_{t \rightarrow 0^+} p(t) u'(t) = 0, \gamma u(1) - \delta \lim_{t \rightarrow 1^-} p(t) u'(t) = 0, \] where \(\alpha, \beta, \gamma, \delta \geq 0\) and \[ \rho := \beta \gamma + \alpha \gamma \int_0^1 {dr \over p(r)} + \alpha \delta > 0. \] With an explicit representation of the Green's function of the corresponding homogeneous boundary value problem (where \(\rho\) is arisen), under a suitable assumption on \(p(t), g(t), F(t, u)\), by applying a fixed point theorem of the cone map, some existence and multiplicity results of positive solutions are obtained.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 5134608
zbMATH Keywords: Sturm-Liouville boundary value problem
zbMATH Keywords: multiple positive solutions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5134608