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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a question in the theory of almost
periodic differential equations


Authors: Zuo Sheng Hu and Angelo B. Mingarelli
Journal: Proc. Amer. Math. Soc. 127 (1999), 2665-2670
MSC (1991): Primary 34C27
Published electronically: April 23, 1999
MathSciNet review: 1485481
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Abstract | References | Similar Articles | Additional Information

Abstract: We show that there exists a real homogeneous differential equation of order $n$ with classical almost periodic coefficients such that all solutions are uniformly bounded on the real line yet no non-trivial solution is almost periodic. This now appears to make the search for a Floquet theory of such equations a futile enterprise.


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Additional Information

Zuo Sheng Hu
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6

Angelo B. Mingarelli
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: angelo_mingarelli@carleton.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04738-3
PII: S 0002-9939(99)04738-3
Keywords: Second-order, almost periodic, boundedness
Received by editor(s): October 7, 1997
Published electronically: April 23, 1999
Additional Notes: The second author was partially supported by an NSERC research grant.
Communicated by: Hal L. Smith
Article copyright: © Copyright 1999 American Mathematical Society