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.

We consider the problem

-Δu=u N+2 N-2+λ inΩεω,u>0inΩεω,u=0onΩεω,
where Ω and ω are smooth bounded domains in N , N3, ε>0 and λ. We prove that if the size of the hole ε goes to zero and if, simultaneously, the parameter λ goes to zero at the appropriate rate, then the problem has a solution which blows up at the origin.

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     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},
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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/

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