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

 

Unbounded perturbations of forced harmonic oscillations at resonance


Author: Tung Ren Ding
Journal: Proc. Amer. Math. Soc. 88 (1983), 59-66
MSC: Primary 34C25; Secondary 34E10, 58F30, 70K40
MathSciNet review: 691279
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Abstract: In 1969, A. C. Lazer and D. E. Leach proved an existence theorem for periodic solutions of Duffing's equations with bounded perturbations at resonance. In the present note, with the use of a topological technique, the author extended some results of Lazer and Leach to an $ n$-dimensional Duffing system with unbounded perturbations at resonance.


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

  • [1] A. C. Lazer, On Schauder’s fixed point theorem and forced second-order nonlinear oscillations, J. Math. Anal. Appl. 21 (1968), 421–425. MR 0221026 (36 #4078)
  • [2] Jean Mawhin, An extension of a theorem of A. C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl. 40 (1972), 20–29. MR 0313587 (47 #2141)
  • [3] A. C. Lazer and D. E. Leach, Bounded perturbations of forced harmonic oscillators at resonance, Ann. Mat. Pura Appl. (4) 82 (1969), 49–68. MR 0249731 (40 #2972)
  • [4] L. Césari, Nonlinear problems across a point of resonance for non-self-adjoint systems, Nonlinear Analysis (A Collection of Papers in Honor of Erich H. Rothe, edited by L. Césari, et al.), Academic Press, New York, 1978.
  • [5] Tong Ren Ding, Nonlinear oscillations at a point of resonance, Sci. Sinica Ser. A 25 (1982), no. 9, 918–931. MR 681856 (84c:34058)
  • [6] -, Some fixed point theorems and periodically perturbed non-dissipative system, Ann. of Math. (2) 2 (1981), 281-297.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0691279-X
PII: S 0002-9939(1983)0691279-X
Keywords: Duffing's equations, high dimension, resonance, unbounded perturbations, periodic solutions, existence theorem, topological technique
Article copyright: © Copyright 1983 American Mathematical Society