Non-collision solutions for a second order singular hamiltonian system with weak force
Annales de l'I.H.P. Analyse non linéaire, Volume 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://www.numdam.org/item/AIHPC_1993__10_2_215_0/}
}
TY  - JOUR
AU  - Tanaka, Kazunaga
TI  - Non-collision solutions for a second order singular hamiltonian system with weak force
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1993
DA  - 1993///
SP  - 215
EP  - 238
VL  - 10
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1993__10_2_215_0/
UR  - https://zbmath.org/?q=an%3A0781.58036
UR  - https://www.ams.org/mathscinet-getitem?mr=1220034
LA  - en
ID  - AIHPC_1993__10_2_215_0
ER  - 
%0 Journal Article
%A Tanaka, Kazunaga
%T Non-collision solutions for a second order singular hamiltonian system with weak force
%J Annales de l'I.H.P. Analyse non linéaire
%D 1993
%P 215-238
%V 10
%N 2
%I Gauthier-Villars
%G en
%F 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, Volume 10 (1993) no. 2, pp. 215-238. http://www.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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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