Periodic solutions for singular hamiltonian systems and closed geodesics on non-compact riemannian manifolds
Annales de l'I.H.P. Analyse non linéaire, Volume 17 (2000) no. 1, p. 1-33
@article{AIHPC_2000__17_1_1_0,
author = {Tanaka, Kazunaga},
title = {Periodic solutions for singular hamiltonian systems and closed geodesics on non-compact riemannian manifolds},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Gauthier-Villars},
volume = {17},
number = {1},
year = {2000},
pages = {1-33},
zbl = {0955.37040},
mrnumber = {1743429},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2000__17_1_1_0}
}

Tanaka, Kazunaga. Periodic solutions for singular hamiltonian systems and closed geodesics on non-compact riemannian manifolds. Annales de l'I.H.P. Analyse non linéaire, Volume 17 (2000) no. 1, pp. 1-33. http://www.numdam.org/item/AIHPC_2000__17_1_1_0/

[1] A. Ambrosetti and U. Bessi, Multiple periodic trajectories in a relativistic gravitational field, in: H. Berestycki, J.-M. Coron and I. Ekeland (Eds.), Variational Methods, Birkhäuser, 1990, pp. 373-381. | MR 1205167 | Zbl 0725.34038

[2] A. Ambrosetti and V. Coti Zelati, Closed orbits of fixed energy for singular Hamiltonian systems, Arch. Rat. Mech. Anal. 112 (1990) 339-362. | MR 1077264 | Zbl 0737.70008

[3] A. Ambrosetti and V. Coti Zelati, Periodic Solutions of Singular Lagrangian Systems, Birkhäuser, Boston, 1993. | MR 1267225 | Zbl 0785.34032

[4] A. Ambrosetti and M. Struwe, Periodic motions for conservative systems with singular potentials, NoDEA Nonlinear Differential Equations Appl. 1 (1994) 179- 202. | MR 1273349 | Zbl 0821.34036

[5] A. Bahri and Y.Y. Li, On a min-max procedure for the existence of a positive solution for certain scalar field equations in RN, Revista Mat. Iberoamericana 6 (1990) 1-15. | MR 1086148 | Zbl 0731.35036

[6] A. Bahri and P.L. Lions, Morse index of some min-max critical points. I. Application to multiplicity results, Comm. Pure Appl. Math. 41 (1988) 1027-1037. | MR 968487 | Zbl 0645.58013

[7] A. Bahri and P.L. Lions, On the existence of a positive solution of semilinear elliptic equations in unbounded domains, Ann. Inst. Henri Poincaré, Analyse Non Linéaire 14 (1997) 365-413. | Numdam | MR 1450954 | Zbl 0883.35045

[8] V. Bangert, Closed geodesics on complete surfaces, Math. Ann. 251 (1980) 83- 96. | MR 583827 | Zbl 0422.53024

[9] V. Benci and D. Fortunato, Subharmonic solutions of prescribed minimal period for autonomous differential equations, in: Dell'Antonio and D'Onofrio (Eds.), Recent Advances in Hamiltonian Systems, World Scientific, Singapore, 1986. | MR 902625 | Zbl 0663.70028

[10] V. Benci and F. Giannoni, Periodic solutions of prescribed energy for a class of Hamiltonian systems with singular potentials, J. Differential Equations 82 (1989) 60-70. | MR 1023301 | Zbl 0689.34034

[11] V. Benci and F. Giannoni, On the existence of closed geodesics on noncompact Riemannian manifolds, Duke Math. J. 68 (1992) 195-215. | MR 1191558 | Zbl 0789.53028

[12] V. Coti Zelati, Periodic solutions for a class of planar, singular dynamical systems, J. Math. Pure Appl. 68 (1989) 109-119. | MR 985956 | Zbl 0633.34034

[13] V. Coti Zelati and E. Serra, Collisions and non-collisions solutions for a class of Keplerian-like dynamical systems, Ann. Mat. Pura Appl. 166 (4) (1994) 343-362. | MR 1313812 | Zbl 0832.70009

[14] G. Fang and N. Ghoussoub, Morse-type information on Palais-Smale sequences obtained by min-max principles, Comm. Pure Appl. Math. 47 (1994) 1595-1653. | MR 1303222 | Zbl 0829.58008

[15] C. Greco, Remarks on periodic solutions, with prescribed energy, for singular Hamiltonian systems, Comment. Math. Univ. Carolin. 28 (1987) 661-672. | MR 928681 | Zbl 0678.34052

[16] W. Klingenberg, Lectures on Closed Geodesics, Grundlehren der Math. Wiss. 230, Springer, Berlin, 1978. | MR 478069 | Zbl 0397.58018

[17] A.C. Lazer and S. Solimini, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type, Nonlinear Analysis: T.M.A. 12 (1988) 761-775. | MR 954951 | Zbl 0667.47036

[18] L. Pisani, Periodic solutions with prescribed energy for singular conservative systems involving strong force, Nonlinear Analysis: T.M.A. 21 (1993) 167-179. | MR 1233958 | Zbl 0801.70012

[19] E. Serra and S. Terracini, Noncollision solutions to some singular minimization problems with Keplerian-like potentials, Nonlinear Analysis: T.M.A. 22 (1994) 45- 62. | MR 1256169 | Zbl 0813.70006

[20] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conf. Ser. in Math., Vol. 65, Amer. Math. Soc., Providence, RI, 1986. | MR 845785 | Zbl 0609.58002

[21] K. Tanaka, Morse indices at critical points related to the symmetric mountain pass theorem and applications, Comm. Partial Differential Equations 14 (1989) 99-128. | MR 973271 | Zbl 0669.34035

[22] K. Tanaka, A prescribed energy problem for a singular Hamiltonian system with a weak force, J. Funct. Anal. 113 (1993) 351-390. | MR 1218100 | Zbl 0771.70014

[23] K. Tanaka, A prescribed-energy problem for a conservative singular Hamiltonian system, Arch. Rational Mech. Anal. 128 (1994) 127-164. | MR 1308850 | Zbl 0823.34047

[24] C. Viterbo, Indice de Morse des points critiques obtenus par minimax, Ann. Inst. Henri Poincaré, Analyse non Linéaire 5 (1988) 221-225. | Numdam | MR 954472 | Zbl 0695.58007

[25] G. Thorbergsson, Closed geodesics on non-compact Riemannian manifold, Math. Z. 159 (1978) 249-258. | MR 493872 | Zbl 0358.53027