Opinions About Qualitative Theory Of Differential Inclusion

There many phenomena are uncertain in nature. There are many methods to describe these. We commonly used method of differential inclusions. Differential inclusion theory is an important branch of the non-linear analysis, the existence of solutions of differential inclusions and control of differential inclusion system are the basic content of the theory of differential inclusion. Differential inclusion system is moro inclusive that compared to other systems of differential equations system. It play a very important role in many areas, for example, medical science, physics, biology, engineering and so on. Differential equations system have a close relation with other maths branches:optimization, optimum control and so on. So differential equations system have became the main subject of study today.This article is divided into three chapters.Chapter Ⅰ, we provide an overview of the development of differential inclusions, boundary value problems and controllability, introduce the main result about them.Chapter Ⅱ, we study on impulsive boundary value problems for Sturm-Liouville type differential inclusions. Using condensing mapping fixed-point theorem, we give the existence of the solutions of system.Chapter Ⅲ, we study on approximate controllability for semilinear neutral functional differential inclusion via analytic semigroups. According to theories for multivalued analysis and pixed-point theorem, sufficient conditions for approximate controllability of system are established.