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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 theorem of Favard


Authors: Zuosheng Hu and Angelo B. Mingarelli
Journal: Proc. Amer. Math. Soc. 132 (2004), 417-428
MSC (2000): Primary 34A30, 34K14; Secondary 42A75
Published electronically: September 11, 2003
MathSciNet review: 2022364
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Abstract: We obtain sufficient conditions for the existence of almost periodic solutions of almost periodic linear differential equations thereby extending Favard's classical theorem. These results are meant to complement previous results of the authors who have shown by means of a counterexample that the boundedness of all solutions is not, by itself, sufficient to guarantee the existence of an almost periodic solution to a linear almost periodic differential equation.


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Additional Information

Zuosheng Hu
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: zhu@math.carleton.ca

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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07166-1
PII: S 0002-9939(03)07166-1
Keywords: Almost periodic functions, Favard's Theorem
Received by editor(s): January 30, 2002
Received by editor(s) in revised form: June 20, 2002, September 11, 2002, and September 30, 2002
Published electronically: September 11, 2003
Additional Notes: This research was partially supported by a research grant from NSERC Canada
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2003 American Mathematical Society