Periodic solutions to some \(N\)-body type problems: The fixed energy case. (English) Zbl 0807.70009
The problem of periodic solutions to some \(N\)-body type problem having prescribed energy has been considered in the existing literature under additional symmetry conditions on the potentials. In the present paper, the authors are concerned with nonsymmetrical potentials; their approach follows the ideas introduced in P. Majer and S. Terracini [Arch. Ration. Mech. Anal. 124, No. 4, 381-404 (1993; Zbl 0782.70010)].
Reviewer: V.Marinca (Timişoara)
Citations:
Zbl 0782.70010References:
| [1] | A. Ambrosetti and V. Coti Zelati, Periodic solutions for \(N\)-body type problems , to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire. · Zbl 0829.70006 |
| [2] | A. Ambrosetti and V. Coti Zelati, Closed orbits of fixed energy for singular Hamiltonian systems , Arch. Rational Mech. Anal. 112 (1990), no. 4, 339-362. · Zbl 0737.70008 · doi:10.1007/BF02384078 |
| [3] | A. Ambrosetti and V. Coti Zelati, Closed orbits of fixed energy for a class of \(N\)-body problems , to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire. · Zbl 0771.70010 |
| [4] | A. Bahri and P. H. Rabinowitz, Periodic solutions of Hamiltonian systems of \(3\)-body type , Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), no. 6, 561-649. · Zbl 0745.34034 |
| [5] | V. Benci and F. Giannoni, Periodic solutions of prescribed energy for a class of Hamiltonian systems with singular potentials , J. Differential Equations 82 (1989), no. 1, 60-70. · Zbl 0689.34034 · doi:10.1016/0022-0396(89)90167-8 |
| [6] | U. Bessi and V. Coti Zelati, Symmetries and non-collision closed orbits for planar \(N\)-body type problems , preprint, SISSA, 1990. · Zbl 0715.70016 |
| [7] | V. Coti Zelati, A class of periodic solutions of the \(N\)-body problem , Celestial Mech. Dynam. Astronom. 46 (1989), no. 2, 177-186. · Zbl 0684.70006 · doi:10.1007/BF00053047 |
| [8] | M. Degiovanni and F. Giannoni, Dynamical systems with Newtonian type potentials , Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), no. 3, 467-494. · Zbl 0692.34050 |
| [9] | C. Greco, Periodic solutions of a class of singular Hamiltonian systems , Nonlinear Anal. 12 (1988), no. 3, 259-269. · Zbl 0648.34048 · doi:10.1016/0362-546X(88)90112-5 |
| [10] | P. Majer, Ljusternik-Schnirelman theory with local Palais-Smale condition and singular dynamical systems , Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991), no. 5, 459-476. · Zbl 0749.58046 |
| [11] | P. Majer, Variational methods on manifolds with boundary , preprint, SISSA, 1991. · Zbl 0749.58046 |
| [12] | P. Majer and S. Terracini, Periodic solutions to some \(N\)-body type problems , to appear in Arch. Rational Mech. Anal. · Zbl 0782.70010 · doi:10.1007/BF00375608 |
| [13] | L. Pisani, Periodic solutions with prescribed energy for singular conservative systems involving strong forces , preprint, Scuola Normale Superiore, Pisa, 1991. |
| [14] | E. Serra and S. Terracini, Noncollision solutions to some three-body problems , to appear in Arch. Rational Mech. Anal. · Zbl 0773.70009 · doi:10.1007/BF00380317 |
| [15] | E. Spanier, Algebraic Topology , McGraw-Hill, New York, 1966. · Zbl 0145.43303 |
| [16] | S. Terracini, Second order conservative systems with singular potentials: noncollision periodic solutions to the fixed energy problem , preprint, 1990. |
| [17] | S. Terracini, Multiplicity of periodic solutions with prescribed energy to singular dynamical systems , to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire. · Zbl 0771.34035 |
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