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Asymptotic behavior of solutions of some semilinear functional differential and integro-differential equations with infinite delay in Banach spaces. (English) Zbl 1260.34142

Summary: We prove in this paper the existence and uniqueness of mild solutions to some functional differential and functional integro-differential equations with infinite delay in Banach spaces which approach almost automorphic functions at infinity. We also discuss the existence of S-asymptotically \(\omega\)-periodic mild solutions. The results are new.

MSC:

34K25 Asymptotic theory of functional-differential equations
34K30 Functional-differential equations in abstract spaces
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
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