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On a theorem of Favard
Author(s):
Zuosheng
Hu;
Angelo
B.
Mingarelli
Journal:
Proc. Amer. Math. Soc.
132
(2004),
417-428.
MSC (2000):
Primary 34A30, 34K14;
Secondary 42A75
Posted:
September 11, 2003
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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.
References:
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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:
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
Posted:
September 11, 2003
Additional Notes:
This research was partially supported by a research grant from NSERC Canada
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2003,
American Mathematical Society
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