A classical variational principle for periodic Hamiltonian trajectories
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- by Frank H. Clarke PDF
- Proc. Amer. Math. Soc. 76 (1979), 186-188 Request permission
Abstract:
Using only classical theorems of the calculus of variations, the existence of periodic solutions to Hamilton’s equations on a given convex energy surface is proved.References
- Naum I. Akhiezer, The calculus of variations, A Blaisdell Book in the Pure and Applied Sciences, Blaisdell Publishing Co. (a division of Random House), New York-London, 1962. Translated from the Russian by Aline H. Frink. MR 0142019
- Frank H. Clarke, Periodic solutions to Hamiltonian inclusions, J. Differential Equations 40 (1981), no. 1, 1–6. MR 614215, DOI 10.1016/0022-0396(81)90007-3
- Paul H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), no. 2, 157–184. MR 467823, DOI 10.1002/cpa.3160310203
- Alan Weinstein, Normal modes for nonlinear Hamiltonian systems, Invent. Math. 20 (1973), 47–57. MR 328222, DOI 10.1007/BF01405263 —, Periodic orbits for convex Hamiltonian systems, Ann. of Math. (to appear).
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 186-188
- MSC: Primary 34C35; Secondary 49H05, 58F05
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534415-7
- MathSciNet review: 534415