Approximate controllability for semilinear second-order stochastic evolution systems with infinite delay

In this work, we study the approximate controllability for a class of semilinear second-order stochastic evolution systems with infinite delay. The main technique is the fundamental solution theory constructed through Laplace transformation. Some sufficient conditions for the approximate controllability result is obtained via the so-called resolvent condition and cosine family of linear operators. Duo to the fundamental solution theory applied, the nonlinear terms are only required to be partly uniformly bounded. Finally, an example is provided to illustrate the obtained results.