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.