Stability and almost periodicity of solutions of ill-posed abstract Cauchy problems

deLaubenfels, R.; Phóng, Vũ

doi:10.1090/S0002-9939-97-03575-2

Stability and almost periodicity of solutions of ill-posed abstract Cauchy problems
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by R. deLaubenfels and Vũ Quôc Phóng PDF

Proc. Amer. Math. Soc. 125 (1997), 235-241 Request permission

Abstract:

We give simple spectral sufficient conditions for a solution of the linear abstract Cauchy problem, on a Banach space, to be strongly stable or asymptotically almost periodic, without assuming that the associated operator generates a $C_{0}$-semigroup.

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