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

الملخص EN

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.