Solutions Of Boundary Value Problems For Higher Order Differential Equations By Means Of Fixed Point Theorems

This paper is devoted to study the existence one or multiple solutions of a class of vector-valued function of n-th order three points nonlocal boundary value problem and a class of n-th order nonlocal integral boundary value problem.This paper is divided into four chapters:in the first chapter,research status at home and abroad,background and significance of nonlinear higher order nonlocal boundary value problems is briefly intro-duced,the research contents and main conclusions of this paper are summarized.In the second chapter,we consider the existence of solutions and multiple solutions for a class of vector-valued function of n-th order three-point nonlocal boundary value problem,trans-forming the original system into system of a Hammerstein integral equation,using the properties of Green's function,a suitable cone is defined in a Banach space,by using the complete continuity of operators in the cone,by means of the well known Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem,a wide range of new fixed point theorems for integral operators are obtained,and the practicability of the new fixed point theorems are illustrated with example.In the third chapter,we consider the exis-tence of positive solutions and multiple solutions for a class of n-th order nonlocal integral boundary value problems,transforming the original problem into an integral equation and a second-order nonlocal integral boundary value problem by using the constant variation method and boundary value conditions,the second-order nonlocal integral boundary value problem is transformed into an integral equation by using the Green's function method,constructing a suitable cone in the Banach space,proving the complete continuity of the operator in the cone,by following the famous Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem,a series of new fixed point theorems for integral operators are obtained,and the effectiveness of the new fixed point theorems are illustrated with two examples.In the fourth chapter is summary and prospect.