, Volume 21, Issue 3, pp 261-279
Date: 11 Nov 2012

Positive Solutions of a Third-Order BVP Independent of the Sign of the Green’s Function

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Abstract

A third-order three-point boundary value problem (BVP) is studied, through this work. We derive sufficient conditions that guarantee the positivity of the solution of the corresponding linear boundary value problem (see Proposition 2). Then, based on the classical Guo-Krasnoselskii fixed point theorem, we obtain positive solutions of the nonlinear BVP. The proposed method may be useful, in cases where the Green’s function changes its sign. A BVP that falls in this category is studied through this paper.