Positive solutions of slightly supercritical elliptic equations in symmetric domains
Annales de l'I.H.P. Analyse non linéaire, Volume 21 (2004) no. 5, p. 639-656
@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},
     publisher = {Elsevier},
     volume = {21},
     number = {5},
     year = {2004},
     pages = {639-656},
     doi = {10.1016/j.anihpc.2003.09.004},
     zbl = {02116182},
     mrnumber = {2086752},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIHPC_2004__21_5_639_0/

[1] Atkinson F.V., Peletier L.A., Elliptic equations with nearly critical growth, J. Differential Equations 70 (3) (1987) 349-365. | MR 915493 | Zbl 0657.35058

[2] 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) 253-294. | MR 929280 | Zbl 0649.35033

[3] Bahri A., Li Y.Y., Rey O., On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var. 3 (1) (1995) 67-93. | MR 1384837 | Zbl 0814.35032

[4] Brezis H., Elliptic equations with limiting Sobolev exponents - The impact of topology, Comm. Pure Appl. Math. 39 (S suppl.) (1986) S17-S39. | MR 861481 | Zbl 0601.35043

[5] Brezis H., Peletier L.A., Asymptotics for elliptic equations involving critical growth, in: Colombini , Modica , Spagnolo (Eds.), P.D.E. and the Calculus of Variations, Birkhäuser, Basel, 1989, pp. 149-192. | MR 1034005 | Zbl 0685.35013

[6] Coron J.M., Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris Sér. I Math. 299 (7) (1984) 209-212. | MR 762722 | Zbl 0569.35032

[7] Dancer E.N., A note on an equation with critical exponent, Bull. London Math. Soc. 20 (6) (1988) 600-602. | MR 980763 | Zbl 0646.35027

[8] Dancer E.N., Zhang K., 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. | MR 1780642 | Zbl 0960.35035

[9] Del Pino M., Felmer P., Musso M., Multipeak solutions for super-critical elliptic problems in domains with small holes, J. Differential Equations 182 (2) (2002) 511-540. | MR 1900333 | Zbl 1014.35028

[10] Ding W.Y., Positive solutions of Δu+u(n+2)/(n−2)=0 on contractible domains, J. Partial Differential Equations 2 (4) (1989) 83-88. | Zbl 0694.35067

[11] Han Z.C., 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. | Numdam | MR 1096602 | Zbl 0729.35014

[12] Kazdan J., Warner F.W., Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (5) (1975) 567-597. | MR 477445 | Zbl 0325.35038

[13] Molle R., Passaseo D., 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. | MR 1937113 | Zbl 1010.35043

[14] Molle R., Passaseo D., Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains, C. R. Acad. Sci. Paris Sér. I Math. 335 (12) (2002) 1029-1032. | MR 1955582 | Zbl 1032.35071

[15] R. Molle, D. Passaseo, On the existence of positive solutions of slightly supercritical elliptic equations, preprint. | MR 1989741

[16] R. Molle, D. Passaseo, A finite dimensional reduction method for slightly supercritical elliptic problems, preprint. | MR 2096946

[17] Passaseo D., Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math. 65 (2) (1989) 147-165. | MR 1011429 | Zbl 0701.35068

[18] Passaseo D., Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal. 114 (1) (1993) 97-105. | MR 1220984 | Zbl 0793.35039

[19] Passaseo D., New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations 8 (3) (1995) 577-586. | MR 1306576 | Zbl 0821.35056

[20] Passaseo D., Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J. 92 (2) (1998) 429-457. | MR 1612734 | Zbl 0943.35034

[21] Pohožaev S.I., On the eigenfunctions of the equation Δu+λf(u)=0, Soviet. Math. Dokl. 6 (1965) 1408-1411.

[22] Rey O., 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. | MR 992090 | Zbl 0686.35047

[23] Rey O., A multiplicity result for a variational problem with lack of compactness, Nonlinear Anal. 13 (10) (1989) 1241-1249. | MR 1020729 | Zbl 0702.35101

[24] Rey O., 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. | MR 1040954 | Zbl 0786.35059

[25] Rey O., 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. | MR 1693274 | Zbl 0952.35051

[26] Talenti G., Best constant in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976) 353-372. | MR 463908 | Zbl 0353.46018

[27] Yan S., High-energy solutions for a nonlinear elliptic problem with slightly supercritical exponent, Nonlinear Anal. Ser. A: Theory Methods 38 (4) (1999) 527-546. | MR 1707876 | Zbl 0956.35043