@article{AIHPC_2001__18_2_157_0,
author = {Catrina, Florin and Wang, Zhi-Qiang},
title = {Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in $\mathbf {R}^N$},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {18},
year = {2001},
pages = {157-178},
zbl = {1005.35045},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2001__18_2_157_0}
}
Catrina, Florin; Wang, Zhi-Qiang. Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in $\mathbf {R}^N$. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) pp. 157-178. http://gdmltest.u-ga.fr/item/AIHPC_2001__18_2_157_0/
[1] , Problèmes isopérimétriques de Sobolev, J. Differential Geom. 11 (1976) 573-598. | MR 448404 | Zbl 0371.46011
[2] , , Existence and bifurcation of solutions for an elliptic degenerate problem, J. Differential Equations 134 (1997) 1-25. | MR 1429089 | Zbl 0870.34032
[3] , , A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR 699419 | Zbl 0526.46037
[4] , Existence of many nonequivalent nonradial positive solutions of semilinear elliptic equations on three-dimensional annuli, J. Differential Equations 136 (1997) 136-165. | MR 1443327 | Zbl 0878.35043
[5] , , , Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271-297. | MR 982351 | Zbl 0702.35085
[6] , , , First order interpolation inequalities with weights, Compositio Mathematica 53 (1984) 259-275. | Numdam | MR 768824 | Zbl 0563.46024
[7] , , On the existence of extremal functions for a weighted Sobolev embedding with critical exponent, Cal. Var. and PDEs 8 (1999) 365-387. | MR 1700269 | Zbl 0929.35045
[8] , , Nonlinear elliptic equations on expanding symmetric domains, J. Differential Equations 156 (1999) 153-181. | MR 1701798 | Zbl 0944.35026
[9] , , On the Caffarelli-Kohn-Nirenberg inequalities, C. R. Acad. Sci. Paris Sér. I Math. 300 (2000) 437-442. | Zbl 0954.35050
[10] Catrina F., Wang Z.-Q., On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence) and symmetry of extremal functions, Comm. Pure Appl. Math., in press. | Zbl 1072.35506
[11] , , On the best constant for a weighted Sobolev-Hardy inequality, J. London Math. Soc. 2 (1993) 137-151. | Zbl 0739.26013
[12] , A nonlinear boundary value problem with many positive solutions, J. Differential Equations 54 (1984) 429-437. | MR 760381 | Zbl 0569.35033
[13] , , Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Springer-Verlag, Berlin, 1985. | MR 1036731 | Zbl 0683.35001
[14] , , , Symmetry of positive solutions of nonlinear elliptic equations in Rn, Adv. Math., Suppl. Studies 7A (1981) 369-402. | MR 634248 | Zbl 0469.35052
[15] , , Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998. | Zbl 0361.35003
[16] , Best constant in weighted Sobolev inequality with weights being powers of distance from the origin, J. Inequal. Appl. 1 (1997) 275-292. | MR 1731336 | Zbl 0899.35034
[17] , Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math., 1150, Springer, 1985. | MR 810619 | Zbl 0593.35002
[18] , Uniqueness of positive solutions of Δu−u+up=0 in Rn, Arch. Rat. Mech. Anal. 105 (1989) 243-266. | Zbl 0676.35032
[19] , Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equations 83 (1990) 348-367. | MR 1033192 | Zbl 0748.35013
[20] , Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. Math. 118 (1983) 349-374. | Zbl 0527.42011
[21] , Concentration compactness principle in the calculus of variations. The locally compact case. Part 1, Ann. Inst. H. Poincaré Anal. Nonlinéaire 1 (1984) 109-145. | Numdam | MR 778970 | Zbl 0541.49009
[22] , Concentration compactness principle in the calculus of variations. The limit case. Part 1, Rev. Mat. Ibero. 1.1 (1985) 145-201. | MR 834360 | Zbl 0704.49005
[23] , , Semilinear elliptic equations on annuli in three and higher dimensions, Houston J. Math. 1 (1996) 199-215. | MR 1434392 | Zbl 0862.35036
[24] , , On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 45 (1991) 819-851. | MR 1115095 | Zbl 0754.35042
[25] , The principle of symmetric criticality, Comm. Math. Phys. 69 (1979) 19-30. | MR 547524 | Zbl 0417.58007
[26] , Best constant in Sobolev inequality, Ann. Mat. Pure Appl. 110 (1976) 353-372. | MR 463908 | Zbl 0353.46018
[27] , Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations, J. Differential Equations 159 (1999) 102-137. | MR 1726920 | Zbl 1005.35083
[28] , , Singular minimization problems, J. Differential Equations 161 (2000) 307-320. | MR 1744147 | Zbl 0954.35074
[29] , Minimax Theorems, Birkhäuser, Boston, 1996. | MR 1400007 | Zbl 0856.49001
[30] Willem M., A decomposition lemma and critical minimization problems, preprint. | MR 2056515