The unique symmetric positive solutions for nonlinear fourth order arbitrary two-point boundary value problems: a fixed point theory approach

Abstract

In this paper, we explore the existence and uniqueness of positive solutions for the following nonlinear fourth order ordinary differential equation u^(4)(t)=f(t,u(t)). Here we also demonstrate that under certain assumptions the above boundary value problem exist a unique symmetric positive solution. The analysis of this paper is based on a fixed point theorem in partially ordered metric spaces due to Amini-Harandi and Emami. The results of this paper generalize the results of several authors in literature. Finally, we provide some illustrative examples to support our analytic proof.