Controllability results for second order semilinear functional differential inclusions based on Kuratowski product measures

A second order semilinear impulsive functional differential inclusion with infinite delay in a separable Banach space is considered. Without imposing hypotheses of compactness on the cosine family of opera- tors, sufficient conditions are established for controllability in the case where the multivalued nonlinearity of the inclusion is a weak upper semicontinuous set-contraction. The results are derived by using the theory of generalized inverse operators and developing appropriate computing techniques for the Kuratowski o f product measures of noncompactness; and the main conditions only depend on the local properties of multivalued map on bounded sets.