@article{AIHPC_2004__21_5_639_0,
author = {Molle, Riccardo and Passaseo, Donato},
title = {Positive solutions of slightly supercritical elliptic equations in symmetric domains},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {639--656},
publisher = {Elsevier},
volume = {21},
number = {5},
year = {2004},
doi = {10.1016/j.anihpc.2003.09.004},
mrnumber = {2086752},
zbl = {02116182},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2003.09.004/}
}
TY - JOUR AU - Molle, Riccardo AU - Passaseo, Donato TI - Positive solutions of slightly supercritical elliptic equations in symmetric domains JO - Annales de l'I.H.P. Analyse non linéaire PY - 2004 SP - 639 EP - 656 VL - 21 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2003.09.004/ DO - 10.1016/j.anihpc.2003.09.004 LA - en ID - AIHPC_2004__21_5_639_0 ER -
%0 Journal Article %A Molle, Riccardo %A Passaseo, Donato %T Positive solutions of slightly supercritical elliptic equations in symmetric domains %J Annales de l'I.H.P. Analyse non linéaire %D 2004 %P 639-656 %V 21 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2003.09.004/ %R 10.1016/j.anihpc.2003.09.004 %G en %F AIHPC_2004__21_5_639_0
Molle, Riccardo; Passaseo, Donato. Positive solutions of slightly supercritical elliptic equations in symmetric domains. Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 5, pp. 639-656. doi: 10.1016/j.anihpc.2003.09.004
[1] , , Elliptic equations with nearly critical growth, J. Differential Equations 70 (3) (1987) 349-365. | Zbl | MR
[2] , , On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math. 41 (1988) 253-294. | Zbl | MR
[3] , , , On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var. 3 (1) (1995) 67-93. | Zbl | MR
[4] , Elliptic equations with limiting Sobolev exponents - The impact of topology, Comm. Pure Appl. Math. 39 (S suppl.) (1986) S17-S39. | Zbl | MR
[5] , , Asymptotics for elliptic equations involving critical growth, in: , , (Eds.), P.D.E. and the Calculus of Variations, Birkhäuser, Basel, 1989, pp. 149-192. | Zbl | MR
[6] , Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris Sér. I Math. 299 (7) (1984) 209-212. | Zbl | MR
[7] , A note on an equation with critical exponent, Bull. London Math. Soc. 20 (6) (1988) 600-602. | Zbl | MR
[8] , , Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains, Nonlinear Anal. Ser. A: TMA 41 (5/6) (2000) 745-761. | Zbl | MR
[9] , , , Multipeak solutions for super-critical elliptic problems in domains with small holes, J. Differential Equations 182 (2) (2002) 511-540. | Zbl | MR
[10] , Positive solutions of Δu+u(n+2)/(n−2)=0 on contractible domains, J. Partial Differential Equations 2 (4) (1989) 83-88. | Zbl
[11] , Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (2) (1991) 159-174. | Zbl | MR | Numdam
[12] , , Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (5) (1975) 567-597. | Zbl | MR
[13] , , Positive solutions for slightly super-critical elliptic equations in contractible domains, Preprint Dip. Matem. Univ. Lecce 6 (2001), C. R. Acad. Sci. Paris Sér. I Math. 335 (5) (2002) 459-462. | Zbl | MR
[14] , , Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains, C. R. Acad. Sci. Paris Sér. I Math. 335 (12) (2002) 1029-1032. | Zbl | MR
[15] R. Molle, D. Passaseo, On the existence of positive solutions of slightly supercritical elliptic equations, preprint. | MR
[16] R. Molle, D. Passaseo, A finite dimensional reduction method for slightly supercritical elliptic problems, preprint. | MR
[17] , Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math. 65 (2) (1989) 147-165. | Zbl | MR
[18] , Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal. 114 (1) (1993) 97-105. | Zbl | MR
[19] , New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations 8 (3) (1995) 577-586. | Zbl | MR
[20] , Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J. 92 (2) (1998) 429-457. | Zbl | MR
[21] , On the eigenfunctions of the equation Δu+λf(u)=0, Soviet. Math. Dokl. 6 (1965) 1408-1411.
[22] , Sur un problème variationnel non compact: l'effet de petits trous dans le domaine, C. R. Acad. Sci. Paris Sér. I Math. 308 (12) (1989) 349-352. | Zbl | MR
[23] , A multiplicity result for a variational problem with lack of compactness, Nonlinear Anal. 13 (10) (1989) 1241-1249. | Zbl | MR
[24] , The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1) (1990) 1-52. | Zbl | MR
[25] , The topological impact of critical points at infinity in a variational problem with lack of compactness: the dimension 3, Adv. Differential Equations 4 (4) (1999) 581-616. | Zbl | MR
[26] , Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976) 353-372. | Zbl | MR
[27] , High-energy solutions for a nonlinear elliptic problem with slightly supercritical exponent, Nonlinear Anal. Ser. A: Theory Methods 38 (4) (1999) 527-546. | Zbl | MR
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