Positive Solutions Of Boundary Value Problems For The Nonlocal High-order Differential Equation Systerms

Differential equations have a very important purpose in modern science and practice. In the first stage of differential equations, we often want to establish a differential equation when we meet the rate of the object especially. For example, when we meet the problems of geometry, the temperature, the rules of movement and so on, which are required to establish models. These models are widely used in economic management and engineering, social and other areas. So, differential equations are the powerful tools that we solve practical problems.As the study of differential equations, the boundary value problem has become one of important branchs in the theory of nonlinear differential equations, and it is also a very dynamic and valuable territory. It is very important that we study the qualitative research of differential equations. Because most of the analytical solutons don't describe and only make clear the number of solves and wether the solutons exsited or not, could we find the numerical solutions and make the appropriate judgment. So many of the mathematics workers began to pay attention boundary value problems for the differential equations, and achieved some results, but the results of differential equations systems are not so much.In this paper, we mainly study the existence of boundary value problem for high-order differential equation systems.There are four parts in this paper, the main contents are as following:In the first chapter, the present author mainly introduces the origin of the differential equations boundary value problems, the studies at home and abroad, and the main research problems of the present thesis.In the second chapter, the paper applies the theoretical structure of the theorems to prove the existence of positive solutions of boundary value problems for the four-order non-local differential equations.In the third chapter, the paper constructs the Green function of multiple-point boundary value problems, applies the holder inequalities and Krasnoselskii fixed point theorem to gain the sufficient condition that n-order coupling multiple-point boundary value problems positive solutions.In the last chapter, the paper uses the five functionals fixed point theorem to reseach the boundary value problems of high-order four-points Sturm-Liouville.The author comes to the conclusion that at least three symmetric positive solutions exist.