Non-collision solutions for a second order singular hamiltonian system with weak force
Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 2, pp. 215-238.
@article{AIHPC_1993__10_2_215_0,
author = {Tanaka, Kazunaga},
title = {Non-collision solutions for a second order singular hamiltonian system with weak force},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {215--238},
publisher = {Gauthier-Villars},
volume = {10},
number = {2},
year = {1993},
zbl = {0781.58036},
mrnumber = {1220034},
language = {en},
url = {http://archive.numdam.org/item/AIHPC_1993__10_2_215_0/}
}
Tanaka, Kazunaga. Non-collision solutions for a second order singular hamiltonian system with weak force. Annales de l'I.H.P. Analyse non linéaire, Tome 10 (1993) no. 2, pp. 215-238. http://archive.numdam.org/item/AIHPC_1993__10_2_215_0/

[AC1] A. Ambrosetti and V. Coti ZELATI, Critical points with lack of compactness and applications to singular dynamical system, Annali Mat. Pura Appl., Vol. 149, 1987, pp. 237-259. | MR 932787 | Zbl 0642.58017

[AC2] A. Ambrosetti and V. Coti ZELATI, Periodic solutions of singular dynamical systems, in Periodic solutions of Hamiltonian systems and related topics, P. H. RABINOWITZ et al. Eds., V209, NATO ASI Series, Reidel, 1987, pp. 1-10. | MR 920605 | Zbl 0632.34042

[AC3] A. Ambrosetti and V. Coti ZELATI, Noncollision orbits for a class of Keplerianlike potentials, Ann. Inst. Henri Poincaré, Analyse non linéaire, Vol. 5, 1988, pp. 287-295. | Numdam | MR 954474 | Zbl 0667.58055

[AC4] A. Ambrosetti and V. Coti ZELATI, Perturbation of Hamiltonian systems with Keplerian potentials, Math. Z., Vol. 201, 1989, pp. 227-242. | MR 997224 | Zbl 0653.34032

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

[BR] 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

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

[DG] M. Degiovanni and F. Giannoni, Dynamical systems with Newtonian type potentials, Annali Scuola Norm. Sup. Pisa, Vol. 15, 1988, pp. 467-494. | Numdam | MR 1015804 | Zbl 0692.34050

[DGM] M. Degiovanni, F. Giannoni and A. Marino, Periodic solutions of dynamical systems with Newtonian type potentials, in Periodic solutions of Hamiltonian systems and related topics, P. H. RABINOWITZ et al. Eds., V209, NATO ASI Series, Reidel, 1987, pp. 111-115. | MR 920613 | Zbl 0632.34038

[Go] W.B. Gordon, Conseruative dynamical systems involving strong forces, Trans. Amer. Math. Soc., Vol. 204, 1975, pp. 113-135. | MR 377983 | Zbl 0276.58005

[Gr1] C. Greco, Periodic solutions of a class of singular Hamiltonian systems, Nonlinear Analysis, T.M.A., Vol. 12, 1988, pp. 259-269. | MR 928560 | Zbl 0648.34048

[GR2] C. Greco, Remarks on periodic solutions for some dynamical systems with singularities, in Periodic solutions of Hamiltonian systems and related topics, P. H. RABINOWITZ et al. Eds., V209, NATO ASI Series, Reidel, 1987, pp. 169-173. | MR 920620 | Zbl 0632.34043

[LS] 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., Vol. 12, 1988, pp. 761-775. | MR 954951 | Zbl 0667.47036

[LF] L.A. Lyusternik and A.I. Fet, Variational problems on closed manifolds, Dokl. Akad. Nauk. USSR, N.S., Vol. 81, 1951, pp. 17-18. | MR 44760 | Zbl 0045.20903

[R] 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, 1986. | MR 845785 | Zbl 0609.58002

[Sc] J.T. Schwartz, Nonlinear functional Analysis, Gordon and Breach, New York, 1969. | MR 433481 | Zbl 0203.14501

[ST] E. Serra and S. Terracini, Noncollision solutions to some singular minimization problems with Keplerian-like potentials, preprint. | MR 1256169

[T] K. Tanaka, Morse indices at critical points related to the symmetric mountain pass theorem and applications, Comm. Partial Diff. Eq., Vol. 14, 1989, pp. 99- 128. | MR 973271 | Zbl 0669.34035

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

[BenFo] V. Benci and D. Fortunato, Subharmonic solutions of prescribed minimal period for autonomous differential equations, in Recent advances in Hamiltonian systems. Dell'Antonio e D'Onofrio Eds., World Sci., Singapore, 1986. | MR 902625 | Zbl 0663.70028

[Bea] A. Bealieu, Étude de solutions généralisées pour un système hamiltonien avec potentiel singulier, Duke Math. J., Vol. 67, 1992, pp. 21-37. | MR 1174601 | Zbl 0758.35016

[CS] V. Coti Zelati and E. Serra, Collisions and non-collisions solutions for a class of Keplerian-like dynamical system, preprint. | MR 1313812