Existence Of Three-point Period Boundary Value Problem For Third Order Nonlinear Equation

In this thesis,the third-order nonlinear equations for a class of three-point period boundary value problems is studied by Volterra type integral operator which is used to convert the third-order boundary value problems to the second-order boundary value problems and the relevant preparatory theorems and differential inequality theories to prove the existence of the equations.On this basis,the three-order nonlinear system for third-point period boundary value problems will be researched.This way is also new idea for the study the third-order three-point boundary value problems.There are three parts in this paper:The first chapter introduces the origin and historical development of ordinary differential equations.Secondly,summarizes some ways to solve ordinary differential equations,such as the differential inequality theories,singular perturbation method and Nagumo.Finally,the details of main work and prior knowledge for two,three chapters are provided.The second chapter introduces the proof of three-point period boundary value problem for third order nonlinear equation:x"' = f(t,x,x',x")x(0)= A,x'(-1)= x'(1),x"(-1)= x"(1)Where A is any real number,According to Volterra type integral operator and differential inequality theories,prove the existence of its solution.The third chapter,in order to develop the more extensive discussion of three-point period boundary value problems for the third-order nonlinear equations,on the basis of a single equation conclusion of the second chapter,we will discuss for a class of period boundary value problems for third-order nonlinear system:x"' f(t,x,x',x")x(0)= A,x'(-1)= x'(1),x"(-1)= x"(1)Where x,f and A is an n-dimensional vector.