Three positive solutions of a nonlinear three-point boundary value problem

Abstract

In this paper, existence criteria for three positive solutions of the nonlinear three-point boundary value problem u″(t)+a(t)u′(t)+b(t)u(t)+h(t)f(u)=0, t∈(0,1), u(0)=0, u(1)=αu(η), are established by using the Leggett–Williams fixed point theorem. An example is also included to illustrate the importance of the result obtained.