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.