Solvability And Structure Of The Solutiobn Set For A Class Of Evolution Inclusions

With the increasing progress of science and technology,the theory of differential inclusions is more close to our daily life.Therefore,the number of scholars in this field are increasing.The structure of solution set of the evolution inclusions has become one of the hot topics in the domestic and international research.The last few years,many scholars began to study the problem of topology structure of solution set of evolution inclusions,and obtained a series of scientific research results.First of all,the origin and significance of differential inclusions are briefly introduced.Then,we give the related concepts and some preliminary knowledge.Then we further discusses the existence of solution for integral boundary value conditions of a class of evolution inclusions.The existence of the solution is analyzed by using the fixed point theorem.In the case of set value,we apply continuous selection theorem and Leray-Schauder's theorem respectively to prove the existence of solutions for the convex cases and nonconvex cases.On the basis of the above discussion,the definition of operator K,according to Dunford-Pettis theorem and related knowledge,it is proved that the K-1 is sequentially continuous.Then,we discuss the topological structure of the solution set of the differential inclusion y'(t)+ By(t)?(t,y(t))under certain conditions.We study the topological structure of the solution set under the integral boundary conditions,use homotopy method to prove that the solution set is a R_? set inC(L,R~N).