The Existence And Uniqueness Of The Solution Of Three Order Nonlinear Three Point Boundary Value

This thesis mainly use the differential inequality technique(or called, lower solutions), prove the existence and uniqueness of the solution of the problem of a class of three order nonlinear three point boundary value under certain conditions, and often appear in the actual application with small parameters of a class of singular perturbation of nonlinear three point boundary value problem on this basis, by using the differential inequality and integral operator techniques, by using upper and lower solutions, and differential inequality techniques, to construct the uniformly valid estimation ofsolutions and solutions of three order asymptotic equation.This paper mainly consists of three parts:The first chapter is the introduction,theory development course work and ordinary differential equation and the method of the previous review the background,given the concept of upper and lower solutions and Nagumo conditions,according to the basic lemma results of differential inequality and basic concepts of the second part and the third part will be used.In the second chapther,by using upper and lower solutions method and the differential inequality technique,the application of the integral operator in the specific conditions of the two kind of three order nonlinear the existence and uniqueness of solutions for three point boundary value problems.In the third chapter,by means of integral operator and differential inequality technique,under certain conditions of a class of three order nonlinear existence and uniqueness of solution for the singularly perturbed problem with three point boundary value,get the existence and unique understanding and its asymptotic efficiency estimation.