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Optimal control problem for some integrodifferential equations in Banach spaces

In this work, we study the existence and stability of solutions for an optimal control problem governed by an integrodifferential equation with compact control set in the space L1([0,b];X). The stability results, in the sense of Baire category theory, for optimal control problems are obtained by the theory of set‐valued mapping and the notion of essential solutions for optimal control problems.