Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-99-04738-3
Published electronically: April 23, 1999
MathSciNet review: 1485481
Full-text PDF

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.


References [Enhancements On Off] (What's this?)

  • [1] H. Bohr, Almost periodic functions, Chelsea, New York, 1947. MR 8:512a
  • [2] C.C. Conley and R.K. Miller, Asymptotic stability without uniform stability: almost periodic coefficients, J. Differential Equations, 1 (1965), 333-336. MR 34:1619
  • [3] M.A. Fink, Almost periodic differential equations, Springer-Verlag, New York-Berlin, 1974.
  • [4] A.B. Mingarelli, F.Q. Pu and L. Zheng, A counter-example in the theory of almost periodic differential equations, Rocky Mountain J. of Math. 25 (1995), 437-440. MR 96e:34070

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34C27

Retrieve articles in all journals with MSC (1991): 34C27


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: https://doi.org/10.1090/S0002-9939-99-04738-3
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

American Mathematical Society