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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On almost periodic solutions for undamped systems with almost periodic forcing
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by George Seifert
Proc. Amer. Math. Soc. 31 (1972), 104-108
DOI: https://doi.org/10.1090/S0002-9939-1972-0285772-4
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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
  • Jack K. Hale, Ordinary differential equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. MR 0419901
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 104-108
  • MSC: Primary 34.45
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0285772-4
  • MathSciNet review: 0285772