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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An infinite class of periodic solutions of periodically perturbed Duffing equations at resonance


Author: Tung Ren Ding
Journal: Proc. Amer. Math. Soc. 86 (1982), 47-54
MSC: Primary 34C15; Secondary 34C25, 58F22
MathSciNet review: 663864
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Abstract: In this paper, by using a generalized form of the Poincaré-Birkhoff Theorem, we demonstrate that the Duffing equation

$\displaystyle \frac{{{d^2}x}} {{d{t^2}}} + g(x) = p(t)\quad ( \equiv p(t + 2\pi ))$

may also admit an infinite number of $ 2\pi $-periodic solutions even in a resonance case.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0663864-1
PII: S 0002-9939(1982)0663864-1
Keywords: Duffing equation, resonance, periodic solutions, a generalized Poincaré-Birkhoff Theorem
Article copyright: © Copyright 1982 American Mathematical Society