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Almost periodicity of mild solutions of inhomogeneous periodic cauchy problems

Abstract:

We consider a mild solution u of a well-posed, inhomogeneous, Cauchy problem, u(t)=A(t)u(t)+f(t), on a Banach space X, where A(·) is periodic. For a problem on R+, we show that u is asymptotically almost periodic if f is asymptotically almost periodic, u is bounded, uniformly continuous and totally ergodic, and the spectrum of the monodromy operator V contains only countably many points of the unit circle. For a problem on R, we show that a bounded, uniformly continuous solution u is almost p...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher version

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Publisher copy:
10.1006/jdeq.1998.3610

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Publisher:
Elsevier B.V. Publisher's website
Journal:
JOURNAL OF DIFFERENTIAL EQUATIONS Journal website
Volume:
156
Issue:
2
Pages:
309-327
Publication date:
1999-08-10
DOI:
ISSN:
0022-0396
URN:
uuid:08c5433d-3c69-4060-80e9-9c0f1c7c4e31
Source identifiers:
3348
Local pid:
pubs:3348

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