Abstract
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.
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