A note on the approximate controllability of damped second-order differential inclusions with state-dependent delay

In this paper, we use Bohnenblust-Karlin's fixed point theorem and the theory of strongly continuous cosine families of bounded linear operators to study the approximate controllability of damped second-order differential inclusions with state-dependent delay in Banach spaces. In particular, we obtain a new set of sufficient conditions for the approximate controllability of damped second-order differential inclusions with state-dependent delay under the assumption that the corresponding linear system is approximately controllable. An example is provided to illustrate our main results.