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Periodic solutions of hamiltonian systems

1978; Wiley; Volume: 31; Issue: 2 Linguagem: Inglês

10.1002/cpa.3160310203

1097-0312

Paul H. Rabinowitz,

Advanced Mathematical Modeling in Engineering

Communications on Pure and Applied MathematicsVolume 31, Issue 2 p. 157-184 Article Periodic solutions of hamiltonian systems Paul H. Rabinowitz, Paul H. Rabinowitz University of WisconsinSearch for more papers by this author Paul H. Rabinowitz, Paul H. Rabinowitz University of WisconsinSearch for more papers by this author First published: March 1978 https://doi.org/10.1002/cpa.3160310203Citations: 470AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Seifert, H., Periodische Bewegungen mechanischer Systeme, Math. Z., 51, 1948, pp. 197–216. 2 Berger, M., On a family of periodic solutions of Hamiltonian systems, J. Diff. Eq., 10, 1971, pp. 17–26. 3 Gordon, W. B., A theorem on the existence of periodic solutions to Hamiltonian systems with convex potential, J. Diff. Eq., 10, 1971, pp. 324–335. 4 Clark, D., On periodic solutions of autonomous Hamiltonian systems of ordinary differential equations, Proc. A.M.S. 39, 1973, pp. 579–584. 5 Weinstein, A., Normal modes for nonlinear Hamiltonian systems, Inv. Math., 20, 1973, pp. 47–57. 6 Moser, J., Periodic orbits near an equilibrium and a theorem by Alan Weinstein, Comm. Pure Appl. Math., 29, 1976, pp. 727–747. 7 Chow, S. N., and J. Mallet-Paret, Periodic solutions near an equilibrium of a non-positive definite Hamiltonian system, preprint. 8 Fadell, E. R., and Rabinowitz, P. H., Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, to appear in Inv. Math. 9 Jacobowitz, H., Periodic solutions of x′ + f(x,t) = 0 via the Poincaré-Birkhoff theorem, J. Diff. Eq., 20, 1976, pp. 37–52. 10 Hartman, P., On boundary value problems for superlinear second-order differential equations, to appear Amer. J. of Math. 11 Rabinowitz, P. H., Free vibrations for a semilinear wave equation, Comm. Pure Appl. Math., Vol. 31, 1978, pp. 31–68. 12 Palais, R. S., Critical point theory and the minimax principle, Proc. Symp. Pure Math., 15, A.M.S., Providence, R.I., 1970, pp. 185–212. 13 Amann, H., Lyusternik-Schnirelman theory and nonlinear eigenvalue problems, Math. Ann., 199, 1972, pp. 55–72. 14 Nirenberg, L., On elliptic partial differential equations, Ann. Scuol. Norm. Sup. Pisa, 13(3), 1959, pp. 1–48. 15 Rabinowitz, P. H., Some critical point theorems and applications to semilinear elliptic partial differential equations, to appear Ann. Scuol. Norm. Sup. Pisa. 16 Weinstein, A., Periodic orbits for convex Hamiltonian systems, preprint. Citing Literature Volume31, Issue2March 1978Pages 157-184 ReferencesRelatedInformation