APPROXIMATE CONTROLLABILITY OF SECOND-ORDER IMPULSIVE STOCHASTIC DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

Abstract

In this paper we study a kind of second-order impulsive stochastic differential equations with state-dependent delay in a real separable Hilbert space. Some sufficient conditions for the approximate controllability of this system are formulated and proved under the assumption that the corresponding deterministic linear system is approximately controllable. The results concerning the existence and approximate controllability of mild solutions have been addressed by using strongly continuous cosine families of operators and the contraction mapping principle. At last, an example is given to illustrate the theory.