Recent results concerning the existence and uniqueness of mild and classical solutions for non-local Cauchy problems are extended to the following non-autonomous semilinear integrodifferential equationin a Banach space X, with A(•) the generators of strongly continuous semigroups.The non-local condition can be applied in physics with better effect than the classical Cauchy problem u(0) = u 0 , since more measurements at t i s are allowed.The variation of constants formula for solutions via a resolvent operator is first derived in order to carry out the study.
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Liu et al. (2003) studied this question.
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