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Asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line

Abstract:

Let u be a bounded, uniformly continuous, mild solution of an inhomogeneous Cauchy problem on R+: u′(t) = Au(t) + (Latin small letter o with stroke)(t) (t ≥ 0). Suppose that u has uniformly convergent means, σ(A) ∩ i R is countable, and (Latin small letter o with stroke) is asymptotically almost periodic. Then u asymptotically almost periodic. Related results have been obtained by Ruess and Vũ, and by Basit, using different methods. A direct proof is given of a Tauberian theorem of Batty, van...

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Publication status:
Published

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Publisher copy:
10.1112/S0024609398005657

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
Volume:
31
Issue:
3
Pages:
291-304
Publication date:
1999-05-05
DOI:
EISSN:
1469-2120
ISSN:
0024-6093
URN:
uuid:0ca47293-e973-4368-a154-710e81562195
Source identifiers:
2609
Local pid:
pubs:2609
Language:
English

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