Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 2, pp. 325-340.
@article{AIHPC_2007__24_2_325_0,
     author = {Pistoia, Angela and Weth, Tobias},
     title = {Sign changing bubble tower solutions in a slightly subcritical semilinear {Dirichlet} problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {325--340},
     publisher = {Elsevier},
     volume = {24},
     number = {2},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.03.002},
     mrnumber = {2310698},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.002/}
}
TY  - JOUR
AU  - Pistoia, Angela
AU  - Weth, Tobias
TI  - Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 325
EP  - 340
VL  - 24
IS  - 2
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.002/
DO  - 10.1016/j.anihpc.2006.03.002
LA  - en
ID  - AIHPC_2007__24_2_325_0
ER  - 
%0 Journal Article
%A Pistoia, Angela
%A Weth, Tobias
%T Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 325-340
%V 24
%N 2
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.002/
%R 10.1016/j.anihpc.2006.03.002
%G en
%F AIHPC_2007__24_2_325_0
Pistoia, Angela; Weth, Tobias. Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 2, pp. 325-340. doi : 10.1016/j.anihpc.2006.03.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2006.03.002/

[1] Atkinson F.V., Brezis H., Peletier L.A., Solutions d'équations elliptiques avec exposant de Sobolev critique qui changent de signe, C. R. Acad. Sci. Paris 306 (1988) 711-714. | MR | Zbl

[2] Atkinson F.V., Brezis H., Peletier L.A., Nodal solutions of elliptic equations with critical Sobolev exponents, J. Differential Equations 85 (1990) 151-170. | MR | Zbl

[3] Aubin T., Problèmes isoperimetriques et espaces de Sobolev, J. Differential Geom. 11 (1976) 573-598. | MR | Zbl

[4] Bahri A., Critical Points at Infinity in Some Variational Problems, Pitman Research Notes in Mathematics Series, vol. 182, Longman, 1989. | MR | Zbl

[5] Bahri A., Coron J.M., On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math. 41 (3) (1988) 253-294. | MR | Zbl

[6] Bahri A., Li Y., Rey O., On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var. Partial Differential Equations 3 (1995) 67-93. | MR | Zbl

[7] Bartsch T., Critical point theory on partially ordered Hilbert spaces, J. Funct. Anal. 186 (2001) 117-152. | MR | Zbl

[8] Bartsch T., Wang Z.-Q., On the existence of sign changing solutions for semilinear Dirichlet problems, Topol. Methods Nonlinear Anal. 7 (1996) 115-131. | MR | Zbl

[9] Bartsch T., Weth T., A note on additional properties of sign changing solutions to superlinear elliptic equations, Topol. Methods Nonlinear Anal. 22 (2003) 1-14. | MR | Zbl

[10] Bartsch T., Micheletti A.M., Pistoia A., On the existence and the profile of nodal solutions of elliptic equations involving critical growth, Calc. Var. Partial Differential Equations 26 (3) (2006) 265-282. | MR | Zbl

[11] Ben Ayed M., El Mehdi K., Grossi M., Rey O., A nonexistence result of single peaked solutions to a supercritical nonlinear problem, Comm. Contemp. Math. 5 (2) (2003) 179-195. | MR | Zbl

[12] Bianchi G., Egnell H., A note on the Sobolev inequality, J. Funct. Anal. 100 (1991) 18-24. | MR | Zbl

[13] Brézis H., Peletier L.A., Asymptotics for elliptic equations involving critical growth, in: Partial Differential Equations and the Calculus of Variations, vol. I, Progr. Nonlinear Differential Equations Appl., vol. 1, Birkhäuser, Boston, MA, 1996, pp. 149-192. | MR | Zbl

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

[15] Castro A., Clapp M., The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain, Nonlinearity 16 (2003) 579-590. | MR | Zbl

[16] Castro A., Cossio J., Neuberger J.M., A sign-changing solution for a superlinear Dirichlet problem, Rocky Mountain J. Math. 27 (1997) 1041-1053. | MR | Zbl

[17] Cerami G., Solimini S., Struwe M., Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal. 69 (1986) 298-306. | MR | Zbl

[18] Clapp M., Weth T., Multiple solutions for the Brezis-Nirenberg problem, Adv. Differential Equations 10 (4) (2005) 463-480.

[19] Clapp M., Weth T., Minimal nodal solutions of the pure critical exponent problem on a symmetric domain, Calc. Var. Partial Differential Equations 21 (1) (2004) 1-14. | MR | Zbl

[20] Del Pino M., Dolbeault J., Musso M., “Bubble-tower” radial solutions in the slightly supercritical Brezis-Nirenberg problem, J. Differential Equations 193 (2) (2003) 280-306.

[21] Del Pino M., Dolbeault J., Musso M., The Brezis-Nirenberg problem near criticality in dimension 3, J. Math. Pures Appl. (9) 83 (12) (2004) 1405-1456. | Zbl

[22] Del Pino M., Felmer P., Musso M., Two-bubble solutions in the super-critical Bahri-Coron's problem, Calc. Var. Partial Differential Equations 16 (2003) 113-145.

[23] Del Pino M., Felmer P., Musso M., Multi-bubble solutions for slightly super-critical elliptic problems in domains with symmetries, Bull. London Math. Soc. 35 (2003) 513-521. | MR | Zbl

[24] Del Pino M., Musso M., Pistoia A., Super-critical boundary bubbling in a semilinear Neumann problem, Ann. Inst. H. Poincaré Anal. Non Linéaire 22 (1) (2005) 45-82. | Numdam | MR | Zbl

[25] Ding W.Y., On a conformally invariant elliptic equation on R N , Comm. Math. Phys. 107 (1986) 331-335. | MR | Zbl

[26] Flucher M., Wei J., Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots, Manuscripta Math. 94 (1997) 337-346. | MR | Zbl

[27] Fortunato D., Jannelli E., Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains, Proc. Roy. Soc. Edinburgh 105 (1987) 205-213. | MR | Zbl

[28] Ge Y., Jing R., Pacard F., Bubble towers for supercritical semilinear elliptic equations, J. Funct. Anal. 221 (2) (2005) 251-302. | MR | Zbl

[29] Han Z.C., Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (1991) 159-174. | Numdam | MR | Zbl

[30] Hebey E., Vaugon M., Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth, J. Funct. Anal. 119 (1994) 298-318. | MR | Zbl

[31] Hirano N., Micheletti A.M., Pistoia A., Existence of changing-sign solutions for some critical problems on R N , Comm. Pure Appl. Anal. 4 (1) (2005) 143-164. | MR | Zbl

[32] Kazdan J., Warner F.W., Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (1975) 567-597. | MR | Zbl

[33] Li Y.Y., Prescribing scalar curvature on S n and related problems. I, J. Differential Equations 120 (2) (1995) 319-410. | MR | Zbl

[34] Micheletti A.M., Pistoia A., On the effect of the domain geometry on the existence of sign changing solutions to elliptic problems with critical and supercritical growth, Nonlinearity 17 (3) (2004) 851-866. | MR | Zbl

[35] Molle R., Passaseo D., Positive solutions for slightly super-critical elliptic equations in contractible domains, C. R. Math. Acad. Sci. Paris, Ser. I 335 (2002) 459-462. | MR | Zbl

[36] Müller-Pfeiffer E., On the number of nodal domains for elliptic differential operators, J. London Math. Soc. (2) 31 (1985) 91-100. | MR | Zbl

[37] Musso M., Pistoia A., Multispike solutions for a nonlinear elliptic problem involving critical Sobolev exponent, Indiana Univ. Math. J. 5 (2002) 541-579. | MR | Zbl

[38] A. Pistoia, O. Rey, Multiplicity of solutions to the supercritical Bahri-Coron's problem in pierced domains, Adv. Differential Equations, in press.

[39] Pohožaev S.I., On the eigenfunctions of the equation Δu+λfu=0, Dokl. Akad. Nauk SSSR 165 (1965) 36-39, (in Russian). | MR | Zbl

[40] Rey O., Blow-up points of solutions to elliptic equations with limiting nonlinearity, Differential Integral Equations 4 (1991) 1155-1167. | MR | Zbl

[41] Rey O., The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1990) 1-52. | MR | Zbl

[42] Rey O., Proof of two conjectures of H. Brezis and L.A. Peletier, Manuscripta Math. 65 (1989) 19-37. | MR | Zbl

[43] Talenti G., Best constants in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976) 353-372. | MR | Zbl

Cité par Sources :