Orbital stability for polytropic galaxies

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1. [1] Antonov V.A., Remarks on the problems of stability in stellar dynamics, Soviet Astron. AJ.4 (1961) 859-867. MR131633
2. [2] Antonov V.A., Solution of the problem of stability of a stellar system with the Emden density law and spherical velocity distribution, J. Leningrad Univ. Ser. Mekh. Astro.7 (1962) 135-146. 
3. [3] Barnes J., Goodman J., Hut P., Dynamical instabilities in spherical stellar systems, Astrophys. J.300 (1986) 112-131. MR825605
4. [4] J. Batt, A survey of recent results in the investigation of the Vlasov–Poisson system and questions open for further research, in: L.L. Bonilla, B. Perthame, J. Soler, J.L. Vázquez (Eds.), European Workshop on Kinetic Equations, Book of Abstracts, Granada, Spain, 1996. 
5. [5] Batt J., Faltenbacher W., Horst E., Stationary spherically symmetric models in stellar dynamics, Arch. Rational Mech. Anal.93 (2) (1986) 159-183. Zbl0605.70008MR823117
6. [6] Cazenave T., An Introduction to Nonlinear Schrödinger Equations, Textos de Métodos Matemáticos, vol. 26, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, 1996. 
7. [7] Cazenave T., Lions P.L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Commun. Math. Phys.85 (1982) 549-561. Zbl0513.35007MR677997
8. [8] Dolbeault J., Sánchez O., Soler J., Asymptotic behaviour for the Vlasov–Poisson system in the stellar dynamics case, Arch. Rational Mech. Anal.171 (2004) 301-327. Zbl1057.70009MR2038342
9. [9] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry, I, J. Func. Anal.74 (1987) 160-197. Zbl0656.35122MR901236
10. [10] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry, II, J. Func. Anal.94 (1990) 308-348. Zbl0711.58013MR1081647
11. [11] Guo Y., Variational method for stable polytropic galaxies, Arch. Rational Mech. Anal.150 (1999) 209-224. Zbl0953.70011MR1738118
12. [12] Guo Y., On the generalized Antonov's stability criterion, Contemp. Math.150 (2000) 85-107. Zbl0974.35092MR1777637
13. [13] Guo Y., Rein G., Stable steady states in stellar dynamics, Arch. Rational Mech. Anal.147 (1999) 225-243. Zbl0935.70011MR1709211
14. [14] Guo Y., Rein G., Isotropic steady states in galactic dynamics, Commun. Math. Phys.209 (2001) 607-629. Zbl0974.35093MR1838751
15. [15] Hardy G., Littlewood J.E., Pólya G., Inequalities, Cambridge Mathematical Press, Cambridge, 1952. Zbl0634.26008MR46395
16. [16] Hénon M., Numerical experiments on the stability of spherical stellar systems, Astronom. Astrophys.24 (1973) 229-238. 
17. [17] Lieb E., Loss M., Analysis, American Mathematical Society, Providence, RI, 2001. Zbl0966.26002MR1817225
18. [18] Lions P.L., Perthame B., Propagation of moments and regularity for the 3-dimensional Vlasov–Poisson system, Invent. Math.105 (2) (1991) 415-430. Zbl0741.35061MR1115549
19. [19] Rein G., Reduction and a concentration–compactness principle for energy–Casimir functionals, SIAM J. Math. Anal.33 (2001) 896-912. Zbl1019.35003MR1884728
20. [20] Rein G., Stability of spherically symmetric steady states in galactic dynamics against general perturbations, Arch. Rational Mech. Anal.161 (2002) 27-42. Zbl0998.35041MR1883757
21. [21] Schaeffer J., Steady states in galactic dynamics, Arch. Rational Mech. Anal.172 (2004) 1-19. Zbl1061.85001MR2048565
22. [22] Wan Y.H., On nonlinear stability of isotropic models in stellar dynamics, Arch. Rational Mech. Anal.147 (1999) 245-268. Zbl0931.70012MR1709207
23. [23] Wolansky G., On nonlinear stability of polytropic galaxies, Ann. Inst. H. Poincaré Anal. Non Linéaire16 (1999) 15-48. Zbl0927.70019MR1668556

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