Positive Solutions of a Third-Order Three-Point BVP with Sign-Changing Green’s Function

Abstract

We are concerned with the following third-order three-point boundary value problem:u′′′t=ft, ut, t∈0, 1, u′0=u1=0and u′′η-αu′1=0,whereα∈0, 1andη∈(14+α)/(24-3α),1. Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions onfby using the two-fixed-point theorem due to Avery and Henderson.