Research On The Existence Of Solutions Of Boundary Value Problems For Some Kinds Of Nonlinear Differential System

In this thesis,we study the situation of nonnegative solutions or positive solutions of boundary value problems for several kinds of nonlinear differential system by using topological method and cone theory, the generalized compression image principle Leggett-Williams fixed point theorem and Krasnoselskii fixed point theorem.Accroding to contents,the thesis is divided into four chapters:In the first chapter of this thesis, we mainly introduce the basic application background,the general situation of domestic and foreign research, the arrangement of the paper structure and some fundamental lemmas.The second chapter mainly discuss the exsitence of nonnegative solutions and positive solutions of boundary value problem for second-order ordinary differential system.We firstly study the postive solution of boundary value problem for a class of second-order ordinary differential equations by using topological method and cone theory.Then change the nonlinear item,we study the existence and uniqueness of nonnegative solution of boundary value problem for a class of more general singular second-order systems under some mild conditions by using the generalized compression image principle,and construct the corresponding examples to illustrate the application of the results.The third chapter mainly discuss the exsitence of positive solutions of boundary value problem for third-order ordinary differential equations. By using the method that transform the systems of three-dimensional third-order differential equations into two-dimensional integral-integral equations, we study a class of boundary value problems for three-dimensional third-order differential system, the existence of at least three positive solutions is proved under appropriate conditions by using Leggett-Williams fixed point theorem.In the fourth chapter, we construct a special cone to study the exsitence of positive solutions of boundary value problem for a class of singular fourth-order ordinary differential equations under appropriate conditions by using Krasnoselskii fixed point theorem.The mathod used also is transform equations into integral-integral equation and we show the exsitence of one and two potive solutions.