Existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions

This paper deals with a nonlocal problem governed by the nonlinear differential inclusions with multivalued perturbations in Banach spaces. First using the approach of geometry of Banach space, Hausdorff metric, the measure of noncompactness and fixed point, existence results are obtained. We have removed from previous papers the crucial restriction on the semigroup. Then we establish the asymptotic properties of integral solutions when t → + ∞ . Finally, for illustration, a partial differential equation is worked out.