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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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Unbounded perturbations of forced harmonic oscillations at resonance
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by Tung Ren Ding
Proc. Amer. Math. Soc. 88 (1983), 59-66
DOI: https://doi.org/10.1090/S0002-9939-1983-0691279-X
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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
  • A. C. Lazer, On Schauder’s fixed point theorem and forced second-order nonlinear oscillations, J. Math. Anal. Appl. 21 (1968), 421–425. MR 221026, DOI 10.1016/0022-247X(68)90225-4
  • Jean Mawhin, An extension of a theorem of A. C. Lazer on forced nonlinear oscillations, J. Math. Anal. Appl. 40 (1972), 20–29. MR 313587, DOI 10.1016/0022-247X(72)90025-X
  • 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 249731, DOI 10.1007/BF02410787
    • 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.
  • Tong Ren Ding, Nonlinear oscillations at a point of resonance, Sci. Sinica Ser. A 25 (1982), no. 9, 918–931. MR 681856
    • —, Some fixed point theorems and periodically perturbed non-dissipative system, Ann. of Math. (2) 2 (1981), 281-297.
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Bibliographic Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 88 (1983), 59-66
  • MSC: Primary 34C25; Secondary 34E10, 58F30, 70K40
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0691279-X
  • MathSciNet review: 691279