On the existence of positive solution for second-order multi-points boundary value problems

Authors:
M. A. Niksirat;B. Mehri
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada;Department of Mathematics, Sharif University of Technology, Tehran, Iran
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Existence of a solution of a three-point boundary value problem and the spectral radius of a related linear operator

Nonlinear Analysis: Theory, Methods & Applications

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Abstract

Here we are concerned with the existence of positive solution for autonomous and nonautonomous second-order systems with multi-points boundary conditions. For nonautonomous systems we use the Schauder's fixed point theorem in a suitable Banach space, while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree. In order to verify the obtained results, we have considered some definite systems to verify the results numerically.