Journal article
Almost periodic solutions of first- and second-order Cauchy problems
- Abstract:
- Almost periodicity of solutions of first- and second-order Cauchy problems on the real line is proved under the assumption that the imaginary (resp. real) spectrum of the underlying operator is countable. Related results have been obtained by Ruess-Vũ and Basit. Our proof uses a new idea. It is based on a factorisation method which also gives a short proof (of the vector-valued version) of Loomis' classical theorem, saying that a bounded uniformly continuous function from R into a Banach spaceXwith countable spectrum is almost periodic ifc 0⊄X. Our method can also be used for solutions on the half-line. This is done in a separate paper. © 1997 Academic Press.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.8MB, Terms of use)
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- Publisher copy:
- 10.1006/jdeq.1997.3266
Authors
- Publisher:
- Elsevier
- Journal:
- JOURNAL OF DIFFERENTIAL EQUATIONS More from this journal
- Volume:
- 137
- Issue:
- 2
- Pages:
- 363-383
- Publication date:
- 1997-07-01
- DOI:
- ISSN:
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0022-0396
- Pubs id:
-
27373
- UUID:
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uuid:6c108bfd-0dd7-4dcf-994f-b9beb2d22a03
- Local pid:
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pubs:27373
- Source identifiers:
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27373
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright holder:
- Elsevier BV
- Copyright date:
- 1997
- Notes:
- Copyright 1997 Academic Press. Published by Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/
- Licence:
- Other
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