Three Point Boundary Value Problem For Third Order Differential Equation And Application

In this paper, by the theory of differential inequalities(or upper and lower solutions meth- od),we study the existence and uniqueness solutions of some classes of three point boundary value problems for third-order nonlinear differential equations(without small parameter).At this basic, we study some calsses of singular perturbation of three-point boundary value problem which appear abroad in life and yield area.By making use of Volterra type integral operator and differential inequality techniques, existence and uniqueness and consistent availability estimation of solutions are obtained;Last,we discuss the theory of differential inequalities of some classes of three point linear boundary value problems for third-order differential equations without satisfying nagumo conditions.This paper is made up of four parts:The first part, introduce the circumstance of singular perturbation therom and the work of former,then give the therom of supper and lower solution and nagumo condition, at the same time the result of differential inequality.The second part,At some conditions,by making use of supper and lower solution and dif- ferential inequality techniques integral operator study a class of linear three-point boundary value problems of third order nonlinear differential equation, existence and uniqueness and asymptotic estimmation of solutions are obtained.The third part, at some conditions,by making use of Volterra type integral operator and differential inequality techniques, we study singular perturbation of three-point boundary value problem for third order nonlinear equation existence and uniqueness and consistent availability asymptotic estimmation of solutions are obtained.The fourth part, in virtue of supper and lower solution and differential inequality techniques combined fixed points theory, we study some classes of differenttial system boundary value problem without satisfy nagumo conditions,the existence and uniqueness of solutions are obtained.