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Exact Controllability of Nonlinear Stochastic Impulsive Evolution Differential Inclusions with Infinite Delay in Hilbert Spaces

Abstract. In this paper, we examine the exact controllability problem for a class of nonlinear stochastic impulsive evolution differential inclusions with infinite delay in Hilbert spaces assuming that the evolution system generates a non-compact semigroup. Using the theory of the measure of noncompactness and the fixed-point theorem of condensing multivalued map, we establish a sufficient conditions for the exact controllability. An example is provided to illustrate the proposed result.