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

**[1]**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****[2]**D. E. Leach,*On Poincaré’s perturbation theorem and a theorem of W. S. Loud*, J. Differential Equations**7**(1970), 34–53. MR**0251308****[3]**Rolf Reissig,*Contractive mappings and periodically perturbed non-conservative systems*, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)**58**(1975), no. 5, 696–702 (English, with Italian summary). MR**0430423****[4]**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****[5]**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.**[6]**Tong Ren Ding,*Nonlinear oscillations at a point of resonance*, Sci. Sinica Ser. A**25**(1982), no. 9, 918–931. MR**681856****[7]**Wei Yue Ding,*A generalization of the Poincaré-Birkhoff theorem*, Proc. Amer. Math. Soc.**88**(1983), no. 2, 341–346. MR**695272**, 10.1090/S0002-9939-1983-0695272-2

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0663864-1

Keywords:
Duffing equation,
resonance,
periodic solutions,
a generalized Poincaré-Birkhoff Theorem

Article copyright:
© Copyright 1982
American Mathematical Society