bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Yuan, Pengfei and Zhang, Shiqing:
New Periodic Solutions for N-Body Problems with Weak Force Potentials
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.1, p. 93-112, (English)
pdf (335 Kb), djvu (165 Kb). | MR 2919650 | Zbl 1348.70028

Sunto

In this paper, we apply a variant of the famous Mountain Pass Lemmas of Ambrosetti-Rabinowitz ([5]) and Ambrosetti-Coti Zelati ([2]) with (CPS)c type condition of Cerami-Palais-Smale ([12]) to study the existence of new periodic solutions with a prescribed energy for N-body problems with weak force type potentials.
Referenze Bibliografiche
[1] A. AMBROSETTI - V. COTI ZELATI, Closed orbits of fixed energy for singular Hamiltonian systems, Arch. Rat. Mech. Anal., 112 (1990), 339-362. | fulltext (doi) | MR 1077264 | Zbl 0737.70008
[2] A. AMBROSETTI - V. COTI ZELATI, Closed orbits of fixed energy for a class of N-body problems, Ann. Inst. H. Poincaré, Analyse Non Lineaire, 9 (1992), 187-200, Addendum, Ann. Inst. H. Poincaré, Analyse Non Lineaire, 9 (1992), 337-338. | fulltext EuDML | fulltext (doi) | MR 1168307 | Zbl 0757.70007
[3] A. AMBROSETTI - V. COTI ZELATI, Non-collision periodic solutions for a class of symmetric 3-body type problems. Topol. Methods Nonlinear Anal., 3 (1994),197-207. | fulltext (doi) | MR 1281984 | Zbl 0829.70006
[4] A. AMBROSETTI - V. COTI ZELATI, Periodic solutions for singualr Lagrangian systems, Springer, 1993. | fulltext (doi) | MR 1267225 | Zbl 0785.34032
[5] A. AMBROSETTI - P. H. RABINOWITZ, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381. | fulltext (doi) | MR 370183 | Zbl 0273.49063
[6] A. AMBROSETTI - K. TANAKA - E. VITILLARO, Periodic solutions with prescribed energy for some Keplerian N-body problems, Ann. Inst. H. P. Poincaré Anal. Nonlinaire, 11 (1994), 613-632. | fulltext EuDML | fulltext (doi) | MR 1310624 | Zbl 0855.70006
[7] G. ARIOLI - F. GAZZOLA - S. TERRACINI, Minimization properties of Hill's orbits and applications to some N-body problems, Ann. Inst. H. Poincaré Anal Non Lineaire, 7 (2000), 617-650. | fulltext EuDML | fulltext (doi) | MR 1791880 | Zbl 0977.70006
[8] A. BAHRI - P. H. RABINOWITZ, Periodic solutions of Hamiltonian systems of three body type. Ann. Inst. H. Poincaré Anal. Non Lineaire, 8 (1991), 561-649. | fulltext EuDML | fulltext (doi) | MR 1145561 | Zbl 0745.34034
[9] U. BESSI - V. COTI ZELATI, Symmetries and noncollision closed orbits for planar N-body-type problems, Nonlinear Anal., 16 (1991), 587-598. | fulltext (doi) | MR 1094320 | Zbl 0715.70016
[10] G. BUTTAZZO - M. GIAQUINTA - S. HILDEBRANDT, One-dimensional variational problems, Oxford university press, 1998. | MR 1694383 | Zbl 0915.49001
[11] C. CARMINATI - E. SERE - K. TANAKA, The fixed energy problem for a class of nonconvex singular Hailtonian systems. J. Differential Equation, 230 (2006), 362- 377. | fulltext (doi) | MR 2270557 | Zbl 1104.37039
[12] G. CERAMI, Un criterio di esistenza per i punti critici su variete illimitate, Rend. Acad. Sci. Let. Ist. Lombardo, 112 (1978), 332-336. | MR 581298
[13] K. C. CHANG, Infinite dimensional Morse theory and multiple solution problems, Birkhauser, 1993. | fulltext (doi) | MR 1196690 | Zbl 0779.58005
[14] K. C. CHEN, Existence and minimizing properties of vetrograde orbits to the three-body problems with various choices of masses, Annals of Math., 167 (2008), 325-348. | fulltext (doi) | MR 2415377 | Zbl 1170.70006
[15] K. C. CHEN, Variational methods on periodic and quasi-periodic solutions for the N-body problems, Ergodic theory Dynam. Systems, 23 (2003), 1691-1715. | fulltext (doi) | MR 2032484 | Zbl 1128.70306
[16] A. CHENCINER, Action minimizing solutions of the Newtonian n-body problem: From homology to symmetry, ICM 2002, Vol.3, pp. 279-294, Vol. 1, pp. 641-643. | MR 1957539 | Zbl 1136.70310
[17] A. CHENCINER - R. MONTGOMERY, A remarkable periodic solution of the three body problem in the case of equal masses, Ann. of Math., 152 (2000), 881-901. | fulltext EuDML | fulltext (doi) | MR 1815704 | Zbl 0987.70009
[18] A. CHENCINER, Some facts and more questions about the eight, Topological methods, Variational methods and their Appl., ICM 2002 Satellite Conference on Nonlinear functional Anal., edited by H. Brezis, K. C. Chang, S. J. Li and P. Rabinowitz, 77-88. | MR 2010643 | Zbl 1205.37076
[19] V. COTI ZELATI, Introduction to variational methods and singular lagrangian systems, ICTP Lecture Notes, 1994. | Zbl 0832.70009
[20] V. COTI ZELATI, The periodic solutions of N-body type problems, Ann. Inst. H. Poincaré Anal. Nonlineaire, 7 (1990), 477-492. | fulltext EuDML | fulltext (doi) | MR 1138534 | Zbl 0723.70010
[21] M. DEGIOVANNI - F. GIANNONI, Dynamical systems with Newtonian type potentials, Ann. Sc. Norm. Sup. Pisa, 15 (1989), 467-494. | fulltext EuDML | MR 1015804 | Zbl 0692.34050
[22] G. F. DELL'ANTONIO, Classical solutions of a perturbed N-body system, In Top. Nonlinear Anal, M. Matzeu etc. ed. (Birkhauser, 1997), 1-86. | MR 1453887
[23] I. EKELAND, Convexity methods in Hamiltonian mechanics, Springer, 1990. | fulltext (doi) | MR 1051888 | Zbl 0707.70003
[24] D. FERRARIO - S. TERRACINI, On the existence of collisionless equivariant mini- mizers for the classical n-bodyproblem, Invent. Math., 155 (2004), 305-362. | fulltext (doi) | MR 2031430 | Zbl 1068.70013
[25] N. GHOUSSOUB - D. PREISS, A general mountain pass principle for locating and classifying critical points, Ann. Inst. Henri Poincaré Anal. Non Lineaire, 6 (1989), 321-330. | fulltext EuDML | MR 1030853 | Zbl 0711.58008
[26] W. B. GORDON, A minimizing Property of Keplerian orbits, Amer. J. Math., 99 (1977), 961-971. | fulltext (doi) | MR 502484 | Zbl 0378.58006
[27] W. B. GORDON, Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc., 204 (1975), 113-135. | fulltext (doi) | MR 377983 | Zbl 0276.58005
[28] Y. M. LONG - S. Q. ZHANG, Geometric characterizations for variational minimization solutions of the 3-body problems, Act Math. Sinica, 16 (2000), 579-592. | fulltext (doi) | MR 1813454 | Zbl 0980.70009
[29] P. MAJER - S. TERRACINI, Periodic solutions to some N-body type problems: the fixed energy case. Duke Math. J., 69 (1993), 683-697. | fulltext (doi) | MR 1208817 | Zbl 0807.70009
[30] C. MARCHAL, How the method of minimization of action avoids singularities, Cel. Mech. and Dyn. Astronomy, 83 (2002), 325-323. | fulltext (doi) | MR 1956531 | Zbl 1073.70011
[31] C. MOORE, Braids in classical gravity, Phys. Rev. Lett., 70 (1993), 3675-3679. | fulltext (doi) | MR 1220207 | Zbl 1050.37522
[32] R. PALAIS, The principle of symmetric criticality, Comm. Math. Phys., 69 (1979), 19- 30. | MR 547524 | Zbl 0417.58007
[33] E. SERRA - S. TERRACINI, Collisionless periodic solutions to some 3-body problems, Arch. Rational. Mech. Anal., 120 (1992), 305-325. | fulltext (doi) | MR 1185563 | Zbl 0773.70009
[34] C. SIMO, Dynamical properties of the figure eight solution of the three-body problem, In: Contemp. Math., Vol. 292, Amer. Math. Soc., Providence, RI, 2002, 209-228. | fulltext (doi) | MR 1884902 | Zbl 1151.70316
[35] C. SIMO, New families of solutions in N-body problems, In Progr. Math., 201 (2001), 101-115. | MR 1905315 | Zbl 1101.70009
[36] S. TERRACINI, Multiplicity of periodic solution with prescribed energy to singular dynamical systems. Ann. Inst. H. Poincaré Anal. Nonlinaire, 9 (1992), 597-641. | fulltext EuDML | fulltext (doi) | MR 1198306 | Zbl 0771.34035
[37] A. VENTURELLI, Une caracterisation variationnelle des solutions de Lagrange du problem plan des trois corps, C.R. Acad. Sci. Paris, 332 (2001), 641-644. | fulltext (doi) | MR 1841900 | Zbl 1034.70007
[38] S. Q. ZHANG - Q. ZHOU, A minimizing property of Lagrangian solutions, Acta Math. Sinica, 17 (2001), 497-500. | fulltext (doi) | MR 1852963 | Zbl 0988.70007
[39] S. Q. ZHANG - Q. ZHOU, Variational methods for the choregraphy solution to the three-body problem, Sci. China, 45 (2002), 594-597. | MR 1911174
[40] S. Q. ZHANG - Q. ZHOU - Y. LIU, New periodic solutions for 3-body problems, Cel. Mech., 88 (2004), 365-378. | fulltext (doi) | MR 2054928 | Zbl 1160.70325
[41] W. P. ZIEMER, Weakly differentiable functions, Springer, 1989. | fulltext (doi) | MR 1014685 | Zbl 0692.46022

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali