Apporoximate Controllability Of Second Order Stochastic Differential Inclusions With Nonlocal Condition

In 2015,P.Muthukumar et al discuss approximate controllability of a class of second-order neutral stochastic differential equations with delay and poisson jumps.In specific applications,Controllability of stochastic processes generated by brown-ian motion is more complicationed.This paper studies approximate controllability of second order stochastic differential inclusions with nonlocal condition.In this article,it is supposed that the nonlocal condition is the local incremental condition and local Lipschitz continuous.Through the correlation theorem of sine and cosine,analysis of controllability of second-order stochastic differential equation and operation of calculus,by means of Bohnenblust-Karlin fixed point theorem,It is proved that there are weak solutions in the system studied in this paper,and on the basis of the approximate controllable of the linear part derived the sufficient conditions for approximate controllability of the system.Finally,the approximate controllability of the system is extended to the system with impulsive effect.