A note on periodic solutions of nonautonomous second-order systems
HTML articles powered by AMS MathViewer
- by Chun-Lei Tang and Xing-Ping Wu PDF
- Proc. Amer. Math. Soc. 132 (2004), 1295-1303 Request permission
Abstract:
A multiplicity theorem is obtained for periodic solutions of nonautonomous second-order systems with partially periodic potentials by the minimax methods.References
- M. Willem, Oscillations forcés de systemes hamiltoniens, Public Sémin. Analyse non linéaire Univ. Besancon, 1981.
- Paul H. Rabinowitz, On a class of functionals invariant under a $\textbf {Z}^n$ action, Trans. Amer. Math. Soc. 310 (1988), no. 1, 303–311. MR 965755, DOI 10.1090/S0002-9947-1988-0965755-5
- Kung-Ching Chang, On the periodic nonlinearity and the multiplicity of solutions, Nonlinear Anal. 13 (1989), no. 5, 527–537. MR 993256, DOI 10.1016/0362-546X(89)90062-X
- J. Q. Liu, A generalized saddle point theorem, J. Differential Equations 82 (1989), no. 2, 372–385. MR 1027975, DOI 10.1016/0022-0396(89)90139-3
- Xing-Ping Wu, Periodic solutions for nonautonomous second-order systems with bounded nonlinearity, J. Math. Anal. Appl. 230 (1999), no. 1, 135–141. MR 1669593, DOI 10.1006/jmaa.1998.6181
- Chun-Lei Tang, Periodic solutions for nonautonomous second order systems with sublinear nonlinearity, Proc. Amer. Math. Soc. 126 (1998), no. 11, 3263–3270. MR 1476396, DOI 10.1090/S0002-9939-98-04706-6
- Jean Mawhin and Michel Willem, Critical point theory and Hamiltonian systems, Applied Mathematical Sciences, vol. 74, Springer-Verlag, New York, 1989. MR 982267, DOI 10.1007/978-1-4757-2061-7
- J. Mawhin, Nonlinear oscillations: one hundred years after Liapunov and Poincaré, Z. Angew. Math. Mech. 73 (1993), no. 4-5, T54–T62. Bericht über die Wissenschaftliche Jahrestagung der GAMM (Leipzig, 1992). MR 1221378, DOI 10.1002/zamm.19930730403
- J. Mawhin, Forced second order conservative systems with periodic nonlinearity, Ann. Inst. H. Poincaré C Anal. Non Linéaire 6 (1989), no. suppl., 415–434. Analyse non linéaire (Perpignan, 1987). MR 1019124, DOI 10.1016/S0294-1449(17)30032-X
- A. Fonda and J. Mawhin, Multiple periodic solutions of conservative systems with periodic nonlinearity, Differential equations and applications, Vol. I, II (Columbus, OH, 1988) Ohio Univ. Press, Athens, OH, 1989, pp. 298–304. MR 1026152
Additional Information
- Chun-Lei Tang
- Affiliation: Department of Mathematics, Southwest Normal University, Chongqing 400715, People’s Republic of China
- Email: tangcl@swnu.edu.cn
- Xing-Ping Wu
- Affiliation: Department of Mathematics, Southwest Normal University, Chongqing 400715, People’s Republic of China
- Email: wuxingping@eduwest.com
- Received by editor(s): April 29, 2001
- Published electronically: December 5, 2003
- Additional Notes: Supported by National Natural Science Foundation of China, by Major Project of Science and Technology of MOE, P.R.C. and by the Teaching and Research Award program for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R.C
- Communicated by: Jonathan M. Borwein
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1295-1303
- MSC (2000): Primary 34C25, 47N20, 58E50
- DOI: https://doi.org/10.1090/S0002-9939-03-07185-5
- MathSciNet review: 2053333