On the radiality of constrained minimizers to the Schrödinger-Poisson- Slater energy

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 29, Issue 3, 2012, Pages 369-376

  Georgiev, Vladimir ^a   Prinari, Francesca ^b   Visciglia, Nicola ^a  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF FERRARA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

RADIAL SYMMETRYS; RADIALLY SYMMETRIC;

EID: 84861796150     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2011.12.001     Document Type: Article

References (18)

1. A. Ambrosetti, and G. Prodi A Primer of Nonlinear Analysis Cambridge Studies in Advanced Mathematics vol. 34 1995 Cambridge University Press Cambridge
2. H. Brezis Functional Analysis, Sobolev Spaces and Partial Differential Equations Universitext 2011 Springer New York
3. Benguria, H. Brezis, and E. Lieb The Thomas-Fermi-von Weizsäcker theory of atoms and molecules Comm. Math. Phys. 79 2 1981 167 180
4. J. Bellazzini, and G. Siciliano Stable standing waves for a class of nonlinear Schrödinger-Poisson equations Z. Angew. Math. Phys. 62 2011 267 280
5. J. Bellazzini, and G. Siciliano Scaling properties of functionals and existence of constrained minimizers J. Funct. Anal. 261 2011 2486 2507
6. I. Catto, and P.L. Lions Binding of atoms and stability of molecules in Hartree and Thomas-Fermi type theories. I. A necessary and sufficient condition for the stability of general molecular systems Comm. Partial Differential Equations 17 1992 1051 1110
7. T. Cazenave, and P.L. Lions Orbital stability of standing waves for some nonlinear Schrödinger equations Comm. Math. Phys. 85 1982 549 561
8. V. Coti-Zelati, and M. Esteban Symmetry breaking and multiple solutions for a Neumann problem in an exterior domain Proc. Royal Soc. Edinburgh 116A 1990 327 339
9. M. Esteban Nonsymmetric ground states of symmetric variational problems Comm. Pure and Appl. Math. 44 1991 259 274
10. M. Esteban Rupture de symétrie pour des problémes de Neumann sur-linéaires dans les ouverts extérieur C. R. Acad. Sci. Sér. I 308 1989 281 286
11. B. Gidas, W. Ni, and L. Nirenberg Symmetry and related properties via the maximum principle Comm. Math. Phys. 68 1979 209 243
12. Rn Arch. Ration. Mech. Anal. 105 1989 243 266
13. E. Lieb Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation Stud. Appl. Math. 57 1976/1977 93 105
14. E. Lieb, and M. Loss Analysis Graduate Studies in Mathematics vol. 14 2001 American Mathematical Society Providence, RI
15. O. Lopes, and M. Maris Symmetry of minimizers for some nonlocal variational problems J. Funct. Anal. 254 2008 535 592
16. O. Sanchez, and J. Soler Long-time dynamics of the Schrödinger- Poisson-Slater system J. Statist. Phys. 114 2004 179 204
17. J. Serrin A symmetry problem in potential theory Arch. Ration. Mech. 43 1971 304 318
18. M.I. Weinstein Modulational stability of ground states of nonlinear Schrödinger equations SIAM J. Math. Anal. 16 1985 472 491