Positive solutions for slightly super-critical elliptic equations in contractible domains
[Solutions positives pour l'équation Δu+u(n+2)/(n−2)+ε=0 en ouverts contractibles]
Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 459-462.

On donne des exemples d'ouverts bornés Ω, même contractibles, satisfaisant la propriété suivante : il existe k ¯(Ω) tel que, pour tout kk ¯(Ω), le problème P(ϵ,Ω) ci-dessous, pour ε>0 suffisamment petit, a des solutions qui pour ε→0 explosent exactement en k points. On prouve aussi que ces points convergent vers des points de Ω quand k→∞.

We give examples of bounded domains Ω, even contractible, having the following property: there exists k ¯(Ω) such that, for every integer kk ¯(Ω), problem P(ϵ,Ω) below, for ε>0 small enough, has at least one solution blowing up as ε→0 at exactly k points. We also prove that the blow-up points tend to some points of Ω as k→∞.

Reçu le :
Publié le :
DOI : 10.1016/S1631-073X(02)02502-5
Molle, Riccardo 1 ; Passaseo, Donato 2

1 Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133 Roma, Italy
2 Dipartimento di Matematica “E. De Giorgi”, Università di Lecce, P.O. Box 193, 73100 Lecce, Italy
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Molle, Riccardo; Passaseo, Donato. Positive solutions for slightly super-critical elliptic equations in contractible domains. Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 459-462. doi : 10.1016/S1631-073X(02)02502-5. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02502-5/

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