Existence and Uniqueness of Positive Solutions for Fourth Order Two Point Sturm-Liouville BVP

Abstract

In this thesis, we consider fourth order two point Sturm-Liouville BVP. The main objective of this study was finding the non trivial solution for the homogeneous part of the differential equation by using Greens function properties, we determine the unique solution for the BVP, then by formulating equivalent operator equation prove existence of positive solution by the application of Guo Krasnoselskii fixed point theorem and finally we verify the uniqueness for the equivalent operator equation.