Uniqueness of Positive Solutions for a Class of Fourth‐Order Boundary Value Problems

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.