Some Problems Research On Stochastic Functional Differential Inclusions And Dissipative System

With the develepment of mordern science and technology,the theory of differential inclusions has extensive practical applicationin in many fields such as engineering, economics,optimal control and optimization theory.Differential inclusions is an important branch in the theory of nonlinear analysis,which has close relationship with differential equations,optimal control and optimization theory.Many phenomenons in nature are stochastic,have been influenced by random factors. Stochastic differential inclusions is a new research field,which plays an important role in characterizing many social,physical,biological and engineering problems.The theory of random differential has developed fast with the development of theory of stochastic analysis and differential inclusions.Existence and controllability of solution is a important problems in the theory of stochastic differential inclusions.Functional differential equations is an important branch in the theory of mathematics. A lot of delay dynamic problems appeared in physics,chemistry,biology, economics,people only use functional differential equations if they want to exactly describe these problems.The theory of periodic solutions is a important task of functional differential equations,which attracted many scholars' great interest.It is necessary for us to study the existence and controllability of the solution of stochastic differential inclusions and the existence of periodic solutions for functional differential equations.This Ph.D.thesis is composed of four chapters,which mainly investigated the existence and controllability of the solution of neutral stochastic differential inclusions with infinite delay,the existence of periodic solutions for dissipative neutral delay differential systems with singular potential and p—Laplacian.In the first chapter,we introduced the history background of problems which will be investigated and main results of this paper.In Chapter 2,by using the knowledge of semigroup and fixed point theorem for a condensing map,we discussed the existence of solutions of first order and second order neutral stochastic functional differential inclusions with infinite delay,established the sufficient conditions for the existence of solution,overcame the difficulties when delay is infinite.This complemented some known result of which delay is finite.Chapter 3 mainly studied the controllability of first order and second order neutral stochastic functional differential inclusions with infinite delay,considered the boundary controllability of a kind of stochastic differential inclusions.Sufficient conditions for the controllability are obtained by using semigroup theory and stochastic analysis skill.In the last chapter,we researched the periodic solutions for dissipative neutral differential systems with singular potential and p—Laplacian by using topological degree theory and some analysis skill.Sufficient conditions to guarantee the existence of periodic solution for the system are given under having no restriction on the damping forces.This result improves and generalize the some known result.Our result is new even when p=2.