The Existence Of Solutions For Some Kinds Of Boundary Value Problem Of Differential Equation

Boundary value problem of differential equation arises in various of aspects of ap-plied mathematics and physics,which is one of the most active field of research in d-ifferential equation.It has importantly practical value and theoretical sense in the field of applied mathematics and engineering,such as power system, ecosystem,financial sys-tem,pneumathics and so on.Therefore,drawing the attention of scholars at home and abroad and obtaining new development in all parts.In this paper,the existence of solutions,positive solutions,symmetric positive solutions and anti-periodic solutions for some boundary value problem of differential equation are studied by means of some classical fixed point theorem. This paper contains five chapter-s,which is as follows:In chapter1, some background knowledge of functional differential systems, fractional calculus and fractional differential systems are introduced, and the preliminary knowledge which is necessary in the paper is given.In chapter2, we discuss the existence of positive solutions for a classes of boundary value problems for a coupled system of nonlinear third-order differential equations. Some sufficient conditions that guarantee the existence of positive solutions are given by using Cone expansion-compression theorem.In chapter3, Solutions for a classes of boundary value problem for a coupled system of nonlinear fractional differential equations with integral boundary conditions are discussed. By means of Schauder fixed-point theorem,some existence results for the solution are obtained.In chapter4, we discuss the symmetric positive solutions for a class of fifth-order boundary value problem with p-Laplacian. By means of Leray-Schauder nonlinear alter-native theory,we proved the existence of symmetric positive solutions for the fifth-order boundary value problem with p-Laplacian.In chapter5,we discuss a class of anti-periodic boundary value problem for a third-order differential equation. By means of Schauder’s fixed point theorem and Leray- Schauder nonlinear alternative theory,Some sufficient conditions for the existence of anti-periodic solutions are obtained.