Controllability for Impulsive Semilinear Functional Differential Inclusions with a Non-compact Evolution Operator

We study the controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulsive effects and delay. Assuming a regularity of the multivalued non-linearity perturbation, in term of the Hausdorff measure of noncompactness, we do not require the compactness of the evolution operator generated by the linear part of the inclusion. We find existence results for mild solutions of this problem under various growth conditions of the nonlinear part and of the jump functions. As an example we consider the controllability of an impulsive system governed by a wave equation with delayed feedback.