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Almost periodic solutions for undamped nonhomogeneous delay-differential equations
Author(s):
George
Seifert
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2001-2005.
MSC (2000):
Primary 34K14
Posted:
November 15, 2001
MathSciNet review:
1896034
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Abstract:
We first establish a result giving conditions that certain undamped delay differential equations with almost periodic time dependence have unique almost periodic solutions. Using this result we obtain conditions that a second order scalar nonlinear delay differential equation with almost periodic forcing will have a unique almost periodic solution having saddle-type stability properties. These results use the method of averaging.
References:
-
- 1.
- G. Seifert, On almost periodic solutions for undamped systems with almost periodic forcing, PAMS 31(1) (1972), 104-108. MR 44:2989
- 2.
- -, Almost periodic solutions by the method of averaging, Lecture Notes in Mathematics 243, Proceedings of Japan-US Seminar on Ordinary Differential and Functional Equations, 1971, 123-133, Springer-Verlag, Berlin. MR 52:14485
- 3.
- J.K. Hale, Theory of Functional Differential Equations, Appl. Math. Sci. 3 (1977), Springer-Verlag, N.Y. MR 58:22904
- 4.
- S.N. Chow and J. Mallet-Paret, Integral averaging and bifurcation, J. Diff. Eq. 26 (1977), 112-159. MR 58:7718
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Additional Information:
George
Seifert
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email:
gseifert@iastate.edu
DOI:
10.1090/S0002-9939-01-06279-7
PII:
S 0002-9939(01)06279-7
Received by editor(s):
February 14, 2000
Received by editor(s) in revised form:
January 22, 2001
Posted:
November 15, 2001
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2001,
American Mathematical Society
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