Analysis For Some Stochastic Evolution Systems And Related Topics In Hilbert Spaces

Researching of Stochastic evolution systems in infinite dimension is a hot issue of dynamics and control engineering,it not only has theoretical significance,but also has real applications.This dissertation aims to study the existence,uniqueness,stability and controllability of mild solutions for some stochastic evolution systems in Hilbert spaces.The main work and innovation are as follows:1.The existence,uniqueness and stability to a class of stochastic evolutions systems with delays and Poisson jumps are investigated.By using successive approximation,the existence and uniqueness of mild solutions to stochastic evolutions equations with delays and Poisson jumps are studied under non-Lipschitz conditions,a sufficient conditions to ensure exponential stability in mean square and almost sure exponential stability of mild solutions is given.An example is presented to illustrate the theory;by using Krasnosclskii-Schauder fixed point theorem,the existence of mild solutions to non-autonomous stochastic evolutions equations with delays and Poisson jumps is presented under non-Lipschitz conditions.2.The existence,uniqueness,stability and controllability of mild solutions to a class of stochastic evolution systems with infinite delay are considered.By employing an axiomatic definition of phase spaces and successive approximation,the existence and uniqueness of mild solutions of stochastic evolution equations with infinite delay are proved under non-Lipschitz conditions,the continuous dependence on an initial value is also presented;the exponential stability in mean square and almost sure exponential stability of mild solutions to stochastic evolution equations with infinite delay are given;exact controllability of mild solutions to stochastic evolution systems with infinite delay is proved by means of Leray-Schauder nonlinear alternative theorem.3.The existence and stability of mild solutions to two classes of stochastic integro-differential systems are studied.The existence of mild solutions to a class of stochastic integro-differential system with nonlocal initial condition are investigated by applying Leray-Schauder nonlinear alternative theorem,the theory of operator and analysis,also,a class of stochastic impulsive integro-differential system with nonlocal initial condition is considered;the existence and exponential stability of mild solutions to a class of stochastic integro-differential evolution equations with infinite delay(in distribution)are investigated.Some known results are improved and generalized.4.The existence of square-mean almost automorphic mild solutions to two classes of neutral stochastic evolution equations are proved.A new phase space is constructed on basis of axiomatic defi-nition of phase space,a new theorem of composition of square-mean almost automorphic function is given,and the existence of square-mean almost automorphic mild solutions to stochastic evolution equations with infinite delay are derived by means of fixed point theorem;the existence square-mean almost automorphic mild solutions to a class of neutral non-autonomous stochastic evolution equations are studied by using the theory of operator and fixed point theorem,which enrich the results of existing literatures.5.The existence of mild solutions to a class of second-order neutral stochastic functional dif-ferential equations is studied.When the impulsive functions are Lipschitz continuous and non-Lipschitz continuous,respectively,sufficient conditions for the existence of mild solutions are derived respectively by assuming the boundedness of cosine family and sine family,an example is presented to illustrate the results.