Uniqueness of positive solutions for a class of fourth-order boundary value problems

Abstract

The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem: y(4)(t)=f(t,y(t)), t ∈ [0,1], y(0)=y(1)= y′(0)= y′(1) = 0. Moreover, under certain assumptions, we will prove that the above boundary value problem has a unique symmetric positive solution. Finally, we present some examples and we compare our results with the ones obtained in recent papers. Our analysis relies on a fixed point theorem in partially ordered metric spaces.