A Study Of Existence Results On Two Point Boundary Value Problem By Fixed Point Method, Monotone Iterative Technique And Solution Matching Techniques

ABSTRACT 

The study of existence results on two point boundary value problems by fixed point methods, monotone iterative techniques, matching solution techniques and integral boundary conditions has been put in place in order to provide a broad understanding to the existence of two point boundary value problems by fixed point methods, monotone iterative techniques and solution matching techniques. The two point boundary value problem for ordinary differential equation has an important role in solving boundary value problems of Ordinary second order differential equations. Also play a great role in solving second-order boundary value problem with integral boundary conditions. The solutions of some linear ODE and boundary integral conditions can be denoted by Green‟s Function. Some BVP of nonlinear Differential Equation can be transformed into nonlinear integral equations by the kernel of which are Green‟s Functions of corresponding linear differential equations. The integral can be solved to investigate the property of the positive solutions. The main objective of the study of two point boundary value problems by fixed point methods, monotone iterative techniques, solution matching techniques and integral boundary conditions is to apply in solving positive solutions integral equations and second order differential equation. In this paper we consider the two point boundary value problem for second order linear differential equation (ODE) and integral boundary conditions with some positive solutions. As application, we study the fixed point methods and integral boundary conditions to find the existence of positive solutions.