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Stepanov-like almost automorphic solutions of nonautonomous semilinear evolution equations with delay. (English) Zbl 1162.34063
The authors investigate the existence and uniqueness of Stepanov-like almost automorphic solutions for some nonautonomous semilinear evolution equations with delay. The linear part is assumed to generate an exponentially stable family of evolution and satisfies the well-known “Acquistapace-Terreni” condition. The delayed part is assumed to be Stepanov like almost automorphic in time and Lipschitzian with respect to the second argument. Sufficient conditions are provided to apply the strict contraction in order to show the main result of this work.

MSC:
34K30 Functional-differential equations in abstract spaces
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
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