Multiplicity of periodic solution with prescribed energy to singular dynamical systems

 Access to full text

 Full (PDF)

1. [1] A. Ambrosetti and V. Coti Zelati, Critical Points with Lack of Compactness and Applications to Singular Dynamical Systems, Ann. di Matem. Pura e Appl., Ser. IV, Vol. CIL, 1987, pp. 237-259. Zbl0642.58017MR932787
2. [2] A. Ambrosetti and V. Coti Zelati, Noncollision Orbits for a Class of Keplerian-Like Potentials, Ann. I.H.P. Analyse non linéaire, Vol. 5, 1988, pp. 287-295. Zbl0667.58055MR954474
3. [3] A. Ambrosetti and V. Coti Zelati, Perturbations of Hamiltonian Systems with Keplerian Potentials, Math. Zeit., Vol. 201, 1989, pp. 227-242. Zbl0653.34032MR997224
4. [4] A. Ambrosetti and V. Coti Zelati, Closed Orbits of Fixed Energy for Singular Hamiltonian Systems, Preprint. MR1077264
5. [5] 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. Zbl0681.70018MR987301
6. [6] P. Bartolo, V. Benci and D. Fortunato, Abstract Critical Points Theory and Application to Some Nonlinear Problems with "Strong" Resonance at Infinity, Nonlin. anal. T.M.A., Vol. 7, 1983, pp.981-1012. Zbl0522.58012MR713209
7. [7] V. Benci, A Geometrical Index for a Group S1 and Some Applications to the Study of Periodic Solutions of O.D.E., Comm. Pure Appl. Math., Vol. 34, 1981, pp. 393-432. Zbl0447.34040MR615624
8. [8] V. Benci, On the Critical Point Theory for Indefinite Functionals in Presence of Symmetries, Trans. Am. Math. Soc., Vol. 274, 1982, pp. 533-572. Zbl0504.58014MR675067
9. [9] V. Benci and F. Giannoni, Periodic Solutions of Prescribed Energy for a Class of Hamiltonian Systems with Singular Potentials, J. Differential equations, Vol. 82, 1989, pp. 60-70. Zbl0689.34034MR1023301
10. [10] A. Capozzi, S. Solimini and S. Terracini, On a Class of Dynamical Systems with Singular Potentials, Preprint S.I.S.S.A., Nonlin. Anal. T.M.A. (to appear). Zbl0744.34039
11. [11] V. Coti Zelati, Dynamical Systems with Effective-Like Potentials, Nonlin. Anal. T.M.A., Vol. 12, 1988, pp. 209-222. Zbl0648.34050
12. [12] V. Coti Zelati, Periodic Solutions for a Class of Planar, Singular Dynamical Systems, J. Math. Pures et Appl., T. 68, 1989, pp. 109-119. Zbl0633.34034MR985956
13. [13] M. Degiovanni and F. Giannoni, Dynamical Systems with Newtonian Type Potentials, Ann. Scuola Norm. Sup Pisa, Cl. Sci., Vol. 4, 1989 (to appear). Zbl0692.34050MR993807
14. [14] M. Degiovanni, F. Giannoni and A. Marino, Periodic Solutions of Dynamical Systems with Newtonian Type Potentials, Atti Accad. Naz. Lincei, Rend. Cl. Sc. Fis. Mat. Nat., Vol. 81, 1987, pp. 271-278. Zbl0667.70010MR999819
15. [15] W. Gordon, A minimizing Property of Keplerian Orbits, Amer. J. Math., Vol. 99, 1975, pp. 961-971. Zbl0378.58006MR502484
16. [16] W. Gordon, Conservative Dynamical Systems Involving Strong Forces, Trans. A.M.S., Vol. 204, 1975, pp. 113-135. Zbl0276.58005MR377983
17. [19] L. Ljusternik and L. Schnirelmann., Méthodes topologiques dans les problèmes variaionnels, Hermann, Paris, 1934. Zbl0011.02803JFM60.1228.04
18. [20] J. Moser, Regularization of Kepler's Problem and the Averaging Method on a Maniold, Comm. Pure Appl. Math., Vol. 23, 1970, pp. 609-636. Zbl0193.53803MR269931
19. [21] S. Terracini, An Homotopical Index and Multiplicity of Periodic Solutions to Dynamical Systems with Singular Potentials, J. of Diff. Eq. (to appear). Zbl0774.34028MR1170468
20. [22] S. Terracini, Second Order Conservative Systems with Singular Potentials: Noncollision Periodic Solutions to the Fixed Energy Problem, Preprint, 1990. 
21. [23] S. Terracini, Ph. D. Thesis, Preprint S.I.S.S.A., Trieste, 1990. 

1. Pengfei Yuan, Shiqing Zhang, New Periodic Solutions for N-Body Problems with Weak Force Potentials