Mild solutions to nonlocal impulsive differential inclusions governed by a noncompact semigroup

In this paper, we study the existence of mild solutions to impulsive differential inclusions with nonlocal conditions in general Banach spaces when operator semigroup is not compact. By using measure of noncompactness and multivalued analysis, we give some sufficient conditions on the existence results where the impulsive items and the nonlocal items are compact and Lipschitz continuous, respectively. An example concerning with the partial differential equation is also presented.