Controllability for systems governed by semilinear differential inclusions in a Banach space with a noncompact semigroup

We stydy the controllability problem for a system governed by a semilinear differential inclusion in a Banach space not assuming that the semigroup generated by the linear part is compact. Instead, we suppose that the multivalued nonlinearity satisfies a regularity condition expressed in term of the hausdorff measure of noncompactness. This hypothesis allow us to apply the topological degree theory for condensing operators and to obtain the controllability results for both upper and almost lower semicontinuos types of nonlinearities. As applicatin we consider the controllability for a system governed by a perturbed wave equation