×

Noncollision solutions to some singular minimization problems with Keplerian-like potentials. (English) Zbl 0813.70006

The paper deals with noncollision solutions to some singular minimization problems with Keplerian-like potentials. It is established that in a symmetric setting one can make use of local hypotheses on the potential in order to obtain the existence of at least one noncollision solution for every potential exponent \(\alpha\) belonging to a certain interval. The results have been summarized in the form of theorems; their proofs have been carefully given and the presentation is good. A list of references has been appended ensuring that authors made a careful study of the relevant literature. The paper is useful for those working on dynamic system problems.
Reviewer: B.B.Sharma (Simla)

MSC:

70F05 Two-body problems
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ambrosetti, A.; Coti Zelati, V., Perturbations of Hamiltonian systems with Keplerian potentials, Math. zerit., 201, 227-242, (1989) · Zbl 0653.34032
[2] Degiovanni, M.; Giannoni, F., Dynamical systems with Newtonian type potentials, Annali scu. norm. sup. Pisa cl. sci., 4, 467-494, (1989) · Zbl 0692.34050
[3] Degiovanni, M.; Giannoni, F.; Marino, A., Periodic solutions of dynamical systems with Newtonian type potentials, Atti accad. naz. lincei, rend. cl. sc., LXXXI, 271-278, (1987) · Zbl 0667.70010
[4] Terracini, S., Periodic solutions to singular dynamical systems with Keplerian type potentials, ()
[5] Ambrosetti, A.; Coti Zelati, V., Critical points with lack of compactness and singular dynamical systems, Annali mat. pura appl., 149, 4, 237-259, (1987) · Zbl 0642.58017
[6] Ambrosetti, A.; Coti Zelati, V., Periodic solutions of singular dynamical systems, (), 1-10, NATO ASI series · Zbl 0757.70007
[7] Bahri, A.; Rabinowitz, P.H., A minimax method for a class of Hamiltonian systems with singular potential, J. funct. analysis, 82, 412-428, (1989) · Zbl 0681.70018
[8] Benci, V.; Giannoni, F., A new proof of the existence of a brake orbit, () · Zbl 0674.34034
[9] Capozzi, A.; Solimini, S.; Terracini, S., On a class of dynamical systems with singular potentials, Nonlinear analysis, 16, 805-815, (1991) · Zbl 0744.34039
[10] Greco, C., Periodic solutions of a class of singular Hamiltonian systems, Nonlinear analysis, 12, 259-269, (1988) · Zbl 0648.34048
[11] Moser, J., Regularization of Kepler’s problem and the averaging method on a manifold, Communs pure appl. math., 23, 609-636, (1970) · Zbl 0193.53803
[12] Terracini S., A homotopical index and multiplicity of periodic solutions to dynamical systems with singular potentials, J. diff. Eqns (to appear). · Zbl 0774.34028
[13] Coti Zelati, V., Periodic solutions for a class of planar, singular dynamical systems, J. math. pures appl., 68, 109-119, (1989) · Zbl 0633.34034
[14] Bessi, U.; Coti Zelati, V., Symmetries and noncollision closed orbits for planar N-body type problems, Nonlinear analysis, 16, 587-598, (1991) · Zbl 0715.70016
[15] Gordon, W., Conservative dynamical systems involving strong forces, Trans. am. math. soc., 204, 113-135, (1975) · Zbl 0276.58005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.