  In this paper, we consider a class of second-order evolution differential
inclusions in Hilbert spaces. This paper deals with the approximate
controllability for a class of second-order control systems. First, we
establish a set of sufficient conditions for the approximate controllability
for a class of second-order evolution differential inclusions in Hilbert
spaces. We use Bohnenblust-Karlin's fixed point theorem to prove our main
results. Further, we extend the result to study the approximate controllability
concept with nonlocal conditions and extend the result to study the approximate
controllability for impulsive control systems with nonlocal conditions. An
example is also given to illustrate our main results.
