Existence of positive solutions for multi-point boundary value problems on infinite intervals in Banach spaces

In this paper, the cone theory and Mönch fixed point theorem combined with a monotone iterative technique are used to investigate the positive solutions of a class of boundary problems for second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinit...

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Bibliographic Details
Published in:Applied mathematics and computation 2008-12, Vol.206 (2), p.932-941
Main Author: Zhang, Xingqiu
Format: Article
Language:English
Subjects:
Cone and ordering
Exact sciences and technology
Functional analysis
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Measure of non-compactness
Mönch fixed point theorem
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Partial differential equations, boundary value problems
Positive solutions
Sciences and techniques of general use
Singular differential equation
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In this paper, the cone theory and Mönch fixed point theorem combined with a monotone iterative technique are used to investigate the positive solutions of a class of boundary problems for second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The conditions for the existence of a positive solution are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2008.10.012