System of singular second-order differential equations with integral condition on the positive half-line

In this work, we are concerned with the existence and the multiplicity of nontrivial positive solutions for a boundary value problem of a system of second-order differential equations subject to an integral boundary condition and posed on the positive half-line. The positive nonlinearities depend on...

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Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2013; no. 50; pp. 1 - 42
Main Authors Djebali, Smail, Mebarki, Karima
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2013
Subjects
cone
differential system
fixed point
fixed point theorems
infinite interval
positive solutions
singularity
zima's compactness criterion
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Summary:In this work, we are concerned with the existence and the multiplicity of nontrivial positive solutions for a boundary value problem of a system of second-order differential equations subject to an integral boundary condition and posed on the positive half-line. The positive nonlinearities depend on the solution and their derivatives and may have space singularities. New existence results of single and multiple solutions are obtained by means of the fixed point index theory on special cones in some weighted Banach space. Examples with numerical computations are included to illustrate the obtained existence theorems. This paper surveys and generalizes previous works.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2013.1.50