We consider the problem
@article{ASNSP_2007_5_6_2_331_0, author = {Musso, Monica and Pistoia, Angela}, title = {Persistence of {Coron's} solution in nearly critical problems}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {331--357}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 6}, number = {2}, year = {2007}, mrnumber = {2352522}, zbl = {1147.35041}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2007_5_6_2_331_0/} }
TY - JOUR AU - Musso, Monica AU - Pistoia, Angela TI - Persistence of Coron's solution in nearly critical problems JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2007 SP - 331 EP - 357 VL - 6 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2007_5_6_2_331_0/ LA - en ID - ASNSP_2007_5_6_2_331_0 ER -
%0 Journal Article %A Musso, Monica %A Pistoia, Angela %T Persistence of Coron's solution in nearly critical problems %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2007 %P 331-357 %V 6 %N 2 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2007_5_6_2_331_0/ %G en %F ASNSP_2007_5_6_2_331_0
Musso, Monica; Pistoia, Angela. Persistence of Coron's solution in nearly critical problems. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 6 (2007) no. 2, pp. 331-357. http://www.numdam.org/item/ASNSP_2007_5_6_2_331_0/
[1] Problemes isoperimetriques et espaces de Sobolev, J. Differential Geom. 11 (1976), 573-598. | MR | Zbl
,[2] “Critical Points at Infinity in Some Variational Problems”, Pitman Research Notes in Mathematics Series, Vol. 182, 1989, Longman. | MR | Zbl
,[3] 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 | Zbl
and ,[4] O. Rey, 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
and ,[5] A nonexistence result of single peaked solutions to a supercritical nonlinear problem, Commun. Contemp. Math. 5 (2003), 179-195. | MR | Zbl
, , and ,[6] A note on the Sobolev inequality, J. Funct. Anal. 100 (1991), 18-24. | MR | Zbl
and ,[7] Asymptotic symmetry and local behaviour of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math. 42 (1989), 271-297. | MR | Zbl
, and ,[8] Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris Sér. I Math. 299 (1984), 209-212. | MR | Zbl
,[9] A note on an equation with critical exponent, Bull. London Math. Soc. 20 (1988), 600-602. | MR | Zbl
,[10] Domain variation for certain sets of solutions and applications, Topol. Methods Nonlin. Anal. 7 (1996), 95-113. | MR | Zbl
,[11] Superlinear problems on domains with holes of asymptotic shape and exterior problems, Math. Z. 229 (1998), 475-491. | MR | Zbl
,[12] Two-bubble solutions in the super-critical Bahri-Coron's problem, Calc. Var. Partial Differential Equations 16 (2003), 113-145. | MR | Zbl
, and ,[13] Multi-peak solutions for super-critical elliptic problems in domains with small holes, J. Differential Equations 182 (2002), 511-540. | MR | Zbl
, and ,[14] Multi-bubble solutions for Slightly super-critial ellitpic problems in domains with symmetries, Bull. London Math. Soc. 35 (2003), 513-521. | MR | Zbl
, and ,[15] 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
,[16] Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (1975), 567-597. | MR | Zbl
and ,[17] A criterion for existence of solutions to the supercritical Bahri-Coron's problem, Houston J. Math. 30 (2004), 587-613. | MR | Zbl
and ,[18] Little holes and convergence of solutions of , Nonlinear Anal. 14 (1990), 873-888. | MR | Zbl
,[19] An elliptic problem with critical growth in domains with shrinking holes, J. Differential Equations 198 (2004), 275-300. | MR | Zbl
, and ,[20] Positive solutions for slightly super-critical elliptic equations in contractible domains, C. R. Math. Acad. Sci. Paris 335 (2002), 459-462. | MR | Zbl
and ,[21] Multiplicity of solutions to the supercritical Bahri-Coron's problem in pierced domains, Adv. Differential Equations 11 (2006), 647-666. | MR | Zbl
and ,[22] On the eigenfunctions of the equation , (Russian) Dokl. Akad. Nauk 165 (1965), 36-39. | Zbl
,[23] Proof of two conjectures of H. Brezis and L.A. Peletier, Manuscripta Math. 65 (1989), 19-37. | MR | Zbl
,[24] Sur un probléme variationnel non compact: l'effect de petits trous dans le domain, C.R. Acad. Sci. Paris 308 (1989), 349-352. | MR | Zbl
,[25] Blow-up points of solutions to elliptic equations with limiting nonlinearity, Differential Integral Equations 4 (1991), 1155-1167. | MR | Zbl
,[26] Best constants in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976), 353-372. | MR | Zbl
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