Multiplicity of periodic solution with prescribed energy to singular dynamical systems
Annales de l'I.H.P. Analyse non linéaire, Volume 9 (1992) no. 6, p. 597-641
@article{AIHPC_1992__9_6_597_0,
author = {Terracini, Susanna},
title = {Multiplicity of periodic solution with prescribed energy to singular dynamical systems},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {9},
number = {6},
year = {1992},
pages = {597-641},
zbl = {0771.34035},
mrnumber = {1198306},
language = {en},
url = {http://www.numdam.org/item/AIHPC_1992__9_6_597_0}
}

Terracini, Susanna. Multiplicity of periodic solution with prescribed energy to singular dynamical systems. Annales de l'I.H.P. Analyse non linéaire, Volume 9 (1992) no. 6, pp. 597-641. http://www.numdam.org/item/AIHPC_1992__9_6_597_0/

[1] A. Ambrosetti and V. Coti Zelati, Critical Points with Lack of Compactness and Applications to Singular Dynamical Systems, Ann. di Matem. Pura e Appl., Ser. IV, Vol. CIL, 1987, pp. 237-259. | MR 932787 | Zbl 0642.58017

[2] A. Ambrosetti and V. Coti Zelati, Noncollision Orbits for a Class of Keplerian-Like Potentials, Ann. I.H.P. Analyse non linéaire, Vol. 5, 1988, pp. 287-295. | Numdam | MR 954474 | Zbl 0667.58055

[3] A. Ambrosetti and V. Coti Zelati, Perturbations of Hamiltonian Systems with Keplerian Potentials, Math. Zeit., Vol. 201, 1989, pp. 227-242. | MR 997224 | Zbl 0653.34032

[4] A. Ambrosetti and V. Coti Zelati, Closed Orbits of Fixed Energy for Singular Hamiltonian Systems, Preprint. | MR 1077264

[5] A. Bahri and P.H. Rabinowitz, A Minimax Method for a Class of Hamiltonian Systems with Singular Potentials, J. Funct. Anal., Vol. 82, 1989, pp. 412-428. | MR 987301 | Zbl 0681.70018

[6] P. Bartolo, V. Benci and D. Fortunato, Abstract Critical Points Theory and Application to Some Nonlinear Problems with "Strong" Resonance at Infinity, Nonlin. anal. T.M.A., Vol. 7, 1983, pp.981-1012. | MR 713209 | Zbl 0522.58012

[7] V. Benci, A Geometrical Index for a Group S1 and Some Applications to the Study of Periodic Solutions of O.D.E., Comm. Pure Appl. Math., Vol. 34, 1981, pp. 393-432. | MR 615624 | Zbl 0447.34040

[8] V. Benci, On the Critical Point Theory for Indefinite Functionals in Presence of Symmetries, Trans. Am. Math. Soc., Vol. 274, 1982, pp. 533-572. | MR 675067 | Zbl 0504.58014

[9] V. Benci and F. Giannoni, Periodic Solutions of Prescribed Energy for a Class of Hamiltonian Systems with Singular Potentials, J. Differential equations, Vol. 82, 1989, pp. 60-70. | MR 1023301 | Zbl 0689.34034

[10] A. Capozzi, S. Solimini and S. Terracini, On a Class of Dynamical Systems with Singular Potentials, Preprint S.I.S.S.A., Nonlin. Anal. T.M.A. (to appear). | MR 1106369 | Zbl 0744.34039

[11] V. Coti Zelati, Dynamical Systems with Effective-Like Potentials, Nonlin. Anal. T.M.A., Vol. 12, 1988, pp. 209-222. | MR 926213 | Zbl 0648.34050

[12] V. Coti Zelati, Periodic Solutions for a Class of Planar, Singular Dynamical Systems, J. Math. Pures et Appl., T. 68, 1989, pp. 109-119. | MR 985956 | Zbl 0633.34034

[13] M. Degiovanni and F. Giannoni, Dynamical Systems with Newtonian Type Potentials, Ann. Scuola Norm. Sup Pisa, Cl. Sci., Vol. 4, 1989 (to appear). | Numdam | MR 1015804 | MR 993807 | Zbl 0692.34050

[14] M. Degiovanni, F. Giannoni and A. Marino, Periodic Solutions of Dynamical Systems with Newtonian Type Potentials, Atti Accad. Naz. Lincei, Rend. Cl. Sc. Fis. Mat. Nat., Vol. 81, 1987, pp. 271-278. | MR 999819 | Zbl 0667.70010

[15] W. Gordon, A minimizing Property of Keplerian Orbits, Amer. J. Math., Vol. 99, 1975, pp. 961-971. | MR 502484 | Zbl 0378.58006

[16] W. Gordon, Conservative Dynamical Systems Involving Strong Forces, Trans. A.M.S., Vol. 204, 1975, pp. 113-135. | MR 377983 | Zbl 0276.58005

[19] L. Ljusternik and L. Schnirelmann., Méthodes topologiques dans les problèmes variaionnels, Hermann, Paris, 1934. | JFM 60.1228.04 | Zbl 0011.02803

[20] J. Moser, Regularization of Kepler's Problem and the Averaging Method on a Maniold, Comm. Pure Appl. Math., Vol. 23, 1970, pp. 609-636. | MR 269931 | Zbl 0193.53803

[21] S. Terracini, An Homotopical Index and Multiplicity of Periodic Solutions to Dynamical Systems with Singular Potentials, J. of Diff. Eq. (to appear). | MR 1170468 | Zbl 0774.34028

[22] S. Terracini, Second Order Conservative Systems with Singular Potentials: Noncollision Periodic Solutions to the Fixed Energy Problem, Preprint, 1990.

[23] S. Terracini, Ph. D. Thesis, Preprint S.I.S.S.A., Trieste, 1990.