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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 almost periodic solutions for undamped systems with almost periodic forcing


Author: George Seifert
Journal: Proc. Amer. Math. Soc. 31 (1972), 104-108
MSC: Primary 34.45
MathSciNet review: 0285772
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Abstract: Using the method of averaging, we give sufficient conditions for the existence of an almost periodic solution of an undamped oscillatory system with almost periodic forcing, and show that these can be applied to a Duffing equation with almost periodic forcing provided the nonlinear term is sufficiently small, and the natural frequency of the linear part of the system is included in the set of Fourier exponents of the forcing function.


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

  • [1] Jack K. Hale, Ordinary differential equations, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. Pure and Applied Mathematics, Vol. XXI. MR 0419901 (54 #7918)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0285772-4
PII: S 0002-9939(1972)0285772-4
Keywords: Almost periodic functions, undamped oscillatory systems, method of averaging, Duffing equation
Article copyright: © Copyright 1972 American Mathematical Society