### Controllability for systems governed by second-order differential inclusions with nonlocal conditions

#### Abstract

We study a controllability problem for a system governed by a semilinear second-order differential inclusion involving control perturbations and nonlocal conditions in a Hilbert space. By using the fixed point theory for condensing multimaps, the $(E_0,X_0)$-controllability result for the mentioned problem is proved under the assumption that the corresponding linear system is $(E_0,X_0)$-controllable.

#### Keywords

Controllability; control system; differential inclusion; nonlocal condition; condensing map; fixed point; measure of non-compactness; MNC-estimate

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