Periodic solutions of the second order differential equations with Lipschitzian condition
HTML articles powered by AMS MathViewer
- by Zaihong Wang PDF
- Proc. Amer. Math. Soc. 126 (1998), 2267-2276 Request permission
Abstract:
In this paper, we prove an infinity of periodic solutions to the periodically forced nonlinear Duffing equation $\ddot {x}+g(x)=p(t)$.References
- 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
- R. Reissig, Contraction mappings and periodically perturbed nonconservative systems, Atti Accad.Naz.Lincei (Rend.Cl.Sci) 58 (1975), 696-702.
- Jean Mawhin, Recent trends in nonlinear boundary value problems, VII. Internationale Konferenz über Nichtlineare Schwingungen (Berlin, 1975) Abh. Akad. Wiss. DDR, Abt. Math. Naturwiss. Tech., 1977, vol. 4, Akademie-Verlag, Berlin, 1977, pp. 51–70. MR 469989
- Pierpaolo Omari and Fabio Zanolin, A note on nonlinear oscillations at resonance, Acta Math. Sinica (N.S.) 3 (1987), no. 4, 351–361. MR 930765, DOI 10.1007/BF02559915
- Tong Ren Ding, Nonlinear oscillations at a point of resonance, Sci. Sinica Ser. A 25 (1982), no. 9, 918–931. MR 681856
- Tung Ren Ding, An infinite class of periodic solutions of periodically perturbed Duffing equations at resonance, Proc. Amer. Math. Soc. 86 (1982), no. 1, 47–54. MR 663864, DOI 10.1090/S0002-9939-1982-0663864-1
- Tong Ren Ding, Rita Iannacci, and Fabio Zanolin, Existence and multiplicity results for periodic solutions of semilinear Duffing equations, J. Differential Equations 105 (1993), no. 2, 364–409. MR 1240400, DOI 10.1006/jdeq.1993.1093
- D. Qian, Time-maps and Duffing equations with resonance-acrossing, Scientia Sinica (Series A) (1993), 471-479.
- Dunyuan Hao and Shiwang Ma, Semilinear Duffing equations crossing resonance points, J. Differential Equations 133 (1997), no. 1, 98–116. MR 1426758, DOI 10.1006/jdeq.1996.3193
- 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
- Zaihong Wang
- Affiliation: Department of Mathematics, Capital Normal University, Beijing 100037, China
- Received by editor(s): December 10, 1996
- Additional Notes: This project was supported by NSF of China.
- Communicated by: Hal L. Smith
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2267-2276
- MSC (1991): Primary 34C25; Secondary 34B15
- DOI: https://doi.org/10.1090/S0002-9939-98-04772-8
- MathSciNet review: 1487345