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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
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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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