Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in 𝐑 N
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) no. 2, pp. 157-178. 
@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},
     pages = {157--178},
     publisher = {Elsevier},
     volume = {18},
     number = {2},
     year = {2001},
     zbl = {1005.35045},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2001__18_2_157_0/}
}
TY  - JOUR
AU  - Catrina, Florin
AU  - Wang, Zhi-Qiang
TI  - Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in $\mathbf {R}^N$
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2001
SP  - 157
EP  - 178
VL  - 18
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/item/AIHPC_2001__18_2_157_0/
LA  - en
ID  - AIHPC_2001__18_2_157_0
ER  - 
%0 Journal Article
%A Catrina, Florin
%A Wang, Zhi-Qiang
%T Positive bound states having prescribed symmetry for a class of nonlinear elliptic equations in $\mathbf {R}^N$
%J Annales de l'I.H.P. Analyse non linéaire
%D 2001
%P 157-178
%V 18
%N 2
%I Elsevier
%U http://archive.numdam.org/item/AIHPC_2001__18_2_157_0/
%G en
%F 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) no. 2, pp. 157-178. http://archive.numdam.org/item/AIHPC_2001__18_2_157_0/

[1] Aubin T, Problèmes isopérimétriques de Sobolev, J. Differential Geom. 11 (1976) 573-598. | MR | Zbl

[2] Berestycki H, Esteban M, Existence and bifurcation of solutions for an elliptic degenerate problem, J. Differential Equations 134 (1997) 1-25. | MR | Zbl

[3] Brezis H, Lieb E.H, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR | Zbl

[4] Byeon J, Existence of many nonequivalent nonradial positive solutions of semilinear elliptic equations on three-dimensional annuli, J. Differential Equations 136 (1997) 136-165. | MR | Zbl

[5] Caffarelli L.A, Gidas B, Spruck J, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989) 271-297. | MR | Zbl

[6] Caffarelli L.A, Kohn R, Nirenberg L, First order interpolation inequalities with weights, Compositio Mathematica 53 (1984) 259-275. | Numdam | MR | Zbl

[7] Caldiroli P, Musina R, On the existence of extremal functions for a weighted Sobolev embedding with critical exponent, Cal. Var. and PDEs 8 (1999) 365-387. | MR | Zbl

[8] Catrina F, Wang Z.-Q, Nonlinear elliptic equations on expanding symmetric domains, J. Differential Equations 156 (1999) 153-181. | MR | Zbl

[9] Catrina F, Wang Z.-Q, On the Caffarelli-Kohn-Nirenberg inequalities, C. R. Acad. Sci. Paris Sér. I Math. 300 (2000) 437-442. | Zbl

[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

[11] Chou K.S, Chu C.W, On the best constant for a weighted Sobolev-Hardy inequality, J. London Math. Soc. 2 (1993) 137-151. | Zbl

[12] Coffman C.V, A nonlinear boundary value problem with many positive solutions, J. Differential Equations 54 (1984) 429-437. | MR | Zbl

[13] Dautray R, Lions J.-L, Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 1, Springer-Verlag, Berlin, 1985. | MR | Zbl

[14] Gidas B, Ni W.-M, Nirenberg L, Symmetry of positive solutions of nonlinear elliptic equations in Rn, Adv. Math., Suppl. Studies 7A (1981) 369-402. | MR | Zbl

[15] Gilbarg D, Trudinger N.S, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998. | Zbl

[16] Horiuchi T, Best constant in weighted Sobolev inequality with weights being powers of distance from the origin, J. Inequal. Appl. 1 (1997) 275-292. | MR | Zbl

[17] Kawohl B, Rearrangements and Convexity of Level Sets in PDE, Lecture Notes in Math., 1150, Springer, 1985. | MR | Zbl

[18] Kwong M.K, Uniqueness of positive solutions of Δu−u+up=0 in Rn, Arch. Rat. Mech. Anal. 105 (1989) 243-266. | Zbl

[19] Li Y.Y, Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equations 83 (1990) 348-367. | MR | Zbl

[20] Lieb E.H, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. Math. 118 (1983) 349-374. | Zbl

[21] Lions P.-L, 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 | Zbl

[22] Lions P.-L, Concentration compactness principle in the calculus of variations. The limit case. Part 1, Rev. Mat. Ibero. 1.1 (1985) 145-201. | MR | Zbl

[23] Mizoguchi N, Suzuki T, Semilinear elliptic equations on annuli in three and higher dimensions, Houston J. Math. 1 (1996) 199-215. | MR | Zbl

[24] Ni W.-M, Takagi I, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 45 (1991) 819-851. | MR | Zbl

[25] Palais R, The principle of symmetric criticality, Comm. Math. Phys. 69 (1979) 19-30. | MR | Zbl

[26] Talenti G, Best constant in Sobolev inequality, Ann. Mat. Pure Appl. 110 (1976) 353-372. | MR | Zbl

[27] Wang Z.-Q, Existence and symmetry of multi-bump solutions for nonlinear Schrödinger equations, J. Differential Equations 159 (1999) 102-137. | MR | Zbl

[28] Wang Z.-Q, Willem M, Singular minimization problems, J. Differential Equations 161 (2000) 307-320. | MR | Zbl

[29] Willem M, Minimax Theorems, Birkhäuser, Boston, 1996. | MR | Zbl

[30] Willem M., A decomposition lemma and critical minimization problems, preprint. | MR