Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions

Abstract In this paper, the existence of solutions and optimal state-control pair of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions in abstract spaces are investigated. By using the Krasnoselskii’s fixed point theorem, we first prove the existence of mild solutions of the concerned problem. Then without the Lipschitz continuity of the nonlinearity, the existence of optimal state-control pair of control system governed by impulsive integro-differential evolution equations is presented by constructing minimizing sequences twice. An example is given as an application of the abstract results.