Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T08:00:17.588Z Has data issue: false hasContentIssue false

Multiple closed orbits for N-body-type problems

Published online by Cambridge University Press:  17 April 2009

Shiqing Zhang
Affiliation:
Department of Applied Mathematics, Chongqing University, Chongqing 630044, People's Republic of China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Ambrosetti, A. and Zelati, V. Coti, ‘Closed orbits of fixed energy for a class of N-body problems’, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992), 187200; (Addendum to closed orbits of fixed energy for a class of N-problems, Ann. Inst. H. Poincaré Analyse Nonlineaire 9 (1992), 337–338).CrossRefGoogle Scholar
[2]Ambrosetti, A. and Zelati, V. Coti, ‘Closed orbits of fixed energy for singular Hamiltonian systems’, Arch Rational Mech. Anal. 112 (1990), 339362.CrossRefGoogle Scholar
[3]Ambrosetti, A. and Zelati, V. Coti, Periodic solutions of singular lagrangian systems (Birkhaüser, Boston, 1993).CrossRefGoogle Scholar
[4]Bessi, U. and Zelati, V. Coti, ‘Symmetries and non-collision closed orbits for planar N-body type problems’, Nonlinear Anal. 16 (1991), 587598.CrossRefGoogle Scholar
[5]Zelati, V. Coti, ‘A class of periodic solutions of the N-body problem’, Celestial Mech. Dynam. Astronom. 46 (1989), 177186.CrossRefGoogle Scholar
[6]Zelati, V. Coti, ‘The periodic solutions of the N-body problems’, Ann. Inst. H. Poincaré Anal. Non Linéaire 46 (1989), 177186.Google Scholar
[7]Fadell, E. and Husseini, S., ‘Infinite cuplength in free loop spaces with an application to a problem of the N-body type’, Ann. Inst. H. Poincaré Anal. Non Linéaire 9 (1992), 305319.CrossRefGoogle Scholar
[8]Giannoni, F. and Degiovanni, M., ‘Dynamical system with Newtonian type potentials’, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 15 (1988), 305319.Google Scholar
[9]Groesen, E.W. Van, ‘Analytical min-max methods for Hamiltonian break orbits of prescribed energy’, J. Math Anal. Appl. 132 (1988), 112.CrossRefGoogle Scholar
[10]Majer, P. and Terracini, S., ‘Periodic solutions to some N-body type problems: The fixed energy case’, Duke Math. J. 60 (1993), 683697.Google Scholar
[11]Vitillaro, E., ‘Noncollision periodic solutions of fixed energy for a symmetric N-body type problem’, in Proceedings of the Workshop on Variational and Local Methods in the Study of Hamiltonian Systems (Trieste 1994) (World Scientific, River Edge, NJ, 1995), pp. 202211.Google Scholar
[12]Zhang, S.Q., ‘Multiple closed orbits of fixed energy for N-body-type problems with gravitational potentials’, (preprint, 1993).Google Scholar