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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1983-0691279-X
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.


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Additional Information

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