Approximate controllability of second order semilinear stochastic system with nonlocal conditions

In this paper, the approximate controllability of second order semilinear stochastic system involving nonlocal conditions is studied. By using Sadovskii’s Fixed Point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of second order semilinear stochastic system with nonlocal conditions under the assumption that the corresponding linear system is approximately controllable. Finally, an application to a second order semilinear stochastic system with nonlocal initial condition is provided to illustrate the obtained theory.