Positive solutions of a nonlinear three-point boundary value problem

Abstract

In this paper, by using Krasnoselskii's fixed point theorem in a cone, we study the existence of single and multiple positive solutions to the three-point boundary value problem (BVP) y″(t)+a(t)f(y(t))=0, 0<t<1, y ′(0)=0, y(1)=βy(η), where 0<η<1, 0<β<1 . As an application, we also give some examples to demonstrate our results.