Electron. J. Diff. Equ., Vol. 2010(2010), No. 155, pp. 1-12.

Existence and uniqueness of a positive solution for a third-order three-point boundary-value problem

Alex P. Palamides, Nikolaos M. Stavrakakis

In this work we study a third-order three-point boundary-value problem (BVP). We derive sufficient conditions that guarantee the positivity of the solution of the corresponding linear BVP Then, based on the classical Guo-Krasnosel'skii's fixed point theorem, we obtain positive solutions to the nonlinear BVP. Additional hypotheses guarantee the uniqueness of the solution.

Submitted May 10, 2010. Published October 28, 2010.
Math Subject Classifications: 34B10, 34B18, 34B15, 34G20.
Key Words: Three point singular boundary value problem; positive solutions; third order differential equation; existence; uniqueness; fixed points in cones; Green's functions

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Alex P. Palamides
Technological Educational Institute of Piraeus
Department Electronic Computer Systems Engineering
Athens, Greece
email: palamid@teipir.gr
Nikolaos M. Stavrakakis
Department of Mathematics, National Technical University
Zografou Campus, 157 80 Athens, Greece
email: nikolas@central.ntua.gr

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