@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}, volume = {10}, year = {1993}, pages = {215-238}, mrnumber = {1220034}, zbl = {0781.58036}, language = {en}, url = {http://dml.mathdoc.fr/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) pp. 215-238. http://gdmltest.u-ga.fr/item/AIHPC_1993__10_2_215_0/
[AC1] 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
and[AC2] 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
and[AC3] 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
and[AC4] ZELATI, Perturbation of Hamiltonian systems with Keplerian potentials, Math. Z., Vol. 201, 1989, pp. 227-242. | MR 997224 | Zbl 0653.34032
and[BL] 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
and ,[BR] 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
and ,[C] 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] Dynamical systems with Newtonian type potentials, Annali Scuola Norm. Sup. Pisa, Vol. 15, 1988, pp. 467-494. | Numdam | MR 1015804 | Zbl 0692.34050
and ,[DGM] 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
, and ,[Go] Conseruative dynamical systems involving strong forces, Trans. Amer. Math. Soc., Vol. 204, 1975, pp. 113-135. | MR 377983 | Zbl 0276.58005
,[Gr1] 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] 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] 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
and ,[LF] Variational problems on closed manifolds, Dokl. Akad. Nauk. USSR, N.S., Vol. 81, 1951, pp. 17-18. | MR 44760 | Zbl 0045.20903
and ,[R] 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] Nonlinear functional Analysis, Gordon and Breach, New York, 1969. | MR 433481 | Zbl 0203.14501
,[ST] Noncollision solutions to some singular minimization problems with Keplerian-like potentials, preprint. | MR 1256169
and ,[T] 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] 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] 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
and ,[Bea] 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] Collisions and non-collisions solutions for a class of Keplerian-like dynamical system, preprint. | MR 1313812
and ,