Non-autonomous Integrodifferential Equations with Non-local Conditions
نویسندگان
چکیده
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 equation u′(t) = A(t) [ u(t) + ∫ t 0 F (t, s)u(s) ds ] + f(t, u(t)), 0 ≤ t ≤ T, u(0) + g(t1, . . . , tp, u(t1), . . . , u(tp)) = u0, in 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) = u0, since more measurements at tis 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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