The Schauder Fixed Point Theorem And analysis Method For Solving Positive Solutions For Second Order M-Point Boundary Value Problems

Abstract

This thesis is designed to develop a scheme for finding positive solution of second order m-point boundary value problem by using schauder fixed point theorem and analysis method without the use of super linear and sub linear cases. The mathematical operation which were performed by schauder fixed point theorem and analysis method were deduced from krasoleskii [9] fixed point theorem and some definition of open sets. The discussion of the study were made by considering the well known fixed point theorem due to Krasnoselskii and some definition of open subsets as a preliminary concept. This study asserts the fact that positive solution of second order m-point B.V.P can be obtained without super linear and sub linear cases ant it gives at least two positive solutions to the model.