Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type

In this paper, we deal with the approximate controllability of stochastic evolution inclusions of Clarke’s subdifferential type. Firstly, by using stochastic analysis, nonsmooth analysis, theory of operator semigroups and fixed point theorems of multivalued maps, we show the existence of mild solutions for the stochastic evolution inclusions. Then we provide a sufficient condition to guarantee the approximate controllability of the stochastic evolution inclusions. Actually, our results cover a broader class of inclusion problems involving time depending operators. Finally, an example is included to illustrate the applicability of the main results.