Supercritical elliptic problems in domains with small holes
Annales de l'I.H.P. Analyse non linéaire (2007)
- Volume: 24, Issue: 4, page 507-520
- ISSN: 0294-1449
Access Full Article
topHow to cite
topdel Pino, Manuel, and Wei, Juncheng. "Supercritical elliptic problems in domains with small holes." Annales de l'I.H.P. Analyse non linéaire 24.4 (2007): 507-520. <http://eudml.org/doc/78746>.
@article{delPino2007,
author = {del Pino, Manuel, Wei, Juncheng},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {supercritical Coron's problem; domains with holes; resonant exponents},
language = {eng},
number = {4},
pages = {507-520},
publisher = {Elsevier},
title = {Supercritical elliptic problems in domains with small holes},
url = {http://eudml.org/doc/78746},
volume = {24},
year = {2007},
}
TY - JOUR
AU - del Pino, Manuel
AU - Wei, Juncheng
TI - Supercritical elliptic problems in domains with small holes
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 4
SP - 507
EP - 520
LA - eng
KW - supercritical Coron's problem; domains with holes; resonant exponents
UR - http://eudml.org/doc/78746
ER -
References
top- [1] 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 (1988) 255-294. Zbl0649.35033MR929280
- [2] Brezis H., Elliptic equations with limiting Sobolev exponent – the impact of topology, Comm. Pure Appl. Math.39 (1986). Zbl0601.35043
- [3] Brezis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math.36 (1983) 437-447. Zbl0541.35029MR709644
- [4] Coron J.M., Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris, Ser. I299 (1984) 209-212. Zbl0569.35032MR762722
- [5] Dancer E.N., Real analyticity and non-degeneracy, Math. Ann.325 (2) (2003) 369-392. Zbl1040.35033MR1962054
- [6] J. Dávila, M. del Pino, M. Musso, The supercritical Lane–Emden–Fowler equation in exterior domains, Preprint, 2006. Zbl1137.35023
- [7] 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. Zbl1130.35040
- [8] del Pino M., Felmer P., Musso M., Two-bubble solutions in the super-critical Bahri–Coron's problem, Calc. Var. Partial Differential Equations16 (2) (2003) 113-145. Zbl1142.35421
- [9] del Pino M., Felmer P., Musso M., Multi-peak solutions for super-critical elliptic problems in domains with small holes, J. Differential Equations182 (2) (2002) 511-540. Zbl1014.35028MR1900333
- [10] Ge Y., Jing R., Pacard F., Bubble towers for supercritical semilinear elliptic equations, J. Funct. Anal.221 (2) (2005) 251-302. Zbl1129.35379MR2124865
- [11] M. Grossi, Asymptotic behavior of the Kazdan–Warner solution in the annulus, J. Differential Equations, in press. Zbl1170.35420
- [12] Kato T., Perturbation Theory for Linear Operators, Grundlehren der Mathematischen Wissenschaften, vol. 132, second ed., Springer-Verlag, Berlin, 1976. Zbl0342.47009MR407617
- [13] Kazdan J., Warner F., Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math.28 (5) (1975) 567-597. Zbl0325.35038MR477445
- [14] Khenissy S., Rey O., A criterion for existence of solutions to the supercritical Bahri–Coron's problem, Houston J. Math.30 (2) (2004) 587-613. Zbl1172.35390
- [15] Micheletti A., Pistoia A., On the effect of the domain geometry on the existence of sign changing solutions to elliptic problems with critical and supercritical growth, Nonlinearity17 (3) (2004) 851-866. Zbl1102.35042MR2057131
- [16] Molle R., Passaseo D., Positive solutions of slightly supercritical elliptic equations in symmetric domains, Ann. Inst. H. Poincaré Anal. Non Linéaire21 (5) (2004) 639-656. Zbl1149.35353MR2086752
- [17] Ni W.-M., A nonlinear Dirichlet problem on the unit ball and its applications, Indiana Univ. Math. J.31 (6) (1982) 801-807. Zbl0515.35033MR674869
- [18] Passaseo D., Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal.114 (1) (1993) 97-105. Zbl0793.35039MR1220984
- [19] Passaseo D., Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J.92 (2) (1998) 429-457. Zbl0943.35034MR1612734
- [20] Pohozaev S., Eigenfunctions of the equation , Soviet Math. Dokl.6 (1965) 1408-1411. Zbl0141.30202MR192184
- [21] Rellich F., Störungstheorie der Spektralzerlegung. IV, Math. Ann.117 (1940) 356-382. Zbl0023.13503MR2715
- [22] Rey O., On a variational problem with lack of compactness: the effect of small holes in the domain, C. R. Acad. Sci. Paris Ser. I Math.308 (12) (1989) 349-352. Zbl0686.35047MR992090
- [23] Wei J., Winter M., Critical threshold and stability of cluster solutions for large reaction–diffusion system in , SIAM J. Math. Anal.33 (2002) 1058-1089. Zbl1019.35014
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.