Non- local Higher Order Differential Equations Boundary Value Existence
|School||Hebei University of Science and Technology|
|Keywords||Ordinary Differential Equations Boundary Value Problems Awl Taper tension, compression fixed point theorem Five functionals fixed point theorem Green's function Symmetric positive solutions|
Differential equations in modern science and production practice has a very important purpose. In the early stages of differential equations , differential equations often want to create , especially when it comes to the rate of change , such as when we encounter geometry problems , temperature problems , object movement of the problem , concentration problems, and so need to build a model. This model is widely used in economic management, engineering, social sciences and other fields , from here we can see that the differential equations to solve practical problems a fairly powerful mathematical tool . With the gradual deepening of research on differential equations , nonlinear ordinary differential equation boundary value problem has become an important branch of the theory , but also a very active and fruitful field. Qualitative research on differential equations is very important because most of the analytical solutions of differential equations is not expressed , but only to clarify the existence of the solution and solve for the number of issues such as the future in order to find its numerical solution was the corresponding conclusions or make judgments , so many domestic and foreign workers began to focus on the mathematical boundary value problem , and achieved certain results. But for the differential equations is not a lot of research . This thesis is the study of higher order boundary value the existence of positive solutions , the main contents are as follows: 1 , focuses on the origins of the boundary value problem , boundary value problems at home and abroad in the field of Research and Benpian research article content. 2 , the use of degree theory to construct a fixed point index theorem, fourth-order nonlocal equations Boundary Value Problems. 3 , construction of multi-point boundary value corresponding Green function ; using Holder inequality and the taper tension, compression fixed point theorem for n order coupled multi-point boundary value sufficient conditions for existence . 4 , the use of five functionals fixed point theorem and cone fixed point theorem, higher order four-point boundary value problems Sturm-liouville , get at least three symmetric positive solutions conclusion.