An infinite class of periodic solutions of periodically perturbed Duffing equations at resonance
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Abstract:
In this paper, by using a generalized form of the Poincaré-Birkhoff Theorem, we demonstrate that the Duffing equation \[ \frac {{{d^2}x}} {{d{t^2}}} + g(x) = p(t)\quad ( \equiv p(t + 2\pi ))\] may also admit an infinite number of $2\pi$-periodic solutions even in a resonance case.References
- Wei Yue Ding, Fixed points of twist mappings and periodic solutions of ordinary differential equations, Acta Math. Sinica 25 (1982), no. 2, 227–235 (Chinese). MR 677834
- D. E. Leach, On Poincaré’s perturbation theorem and a theorem of W. S. Loud, J. Differential Equations 7 (1970), 34–53. MR 251308, DOI 10.1016/0022-0396(70)90122-1
- Rolf Reissig, Contractive mappings and periodically perturbed non-conservative systems, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 58 (1975), no. 5, 696–702 (English, with Italian summary). MR 430423
- 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, non-linear analysis (A Collection of Papers in Honor of Erich H. Rothe), edited by L. Césari et al., Academic Press, New York, 1978, pp. 43-67.
- Tong Ren Ding, Nonlinear oscillations at a point of resonance, Sci. Sinica Ser. A 25 (1982), no. 9, 918–931. MR 681856
- Wei Yue Ding, A generalization of the Poincaré-Birkhoff theorem, Proc. Amer. Math. Soc. 88 (1983), no. 2, 341–346. MR 695272, DOI 10.1090/S0002-9939-1983-0695272-2
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 47-54
- MSC: Primary 34C15; Secondary 34C25, 58F22
- DOI: https://doi.org/10.1090/S0002-9939-1982-0663864-1
- MathSciNet review: 663864