EXISTENCE OF MILD SOLUTIONS IN THE α-NORM FOR SOME PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

Abstract

In this work, we discuss the existence of mild solutions in the α-norm for some partial functional integrodifferential equations with infinite delay. We assume that the linear part generates an analytic semigroup on a Banach space X and the nonlinear part is a Lipschitz continuous function with respect to the fractional power norm of the linear part.

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