Comptes Rendus
Partial Differential Equations
On trichotomy of positive singular solutions associated with the Hardy–Sobolev operator
[Sur la trichotomie des solutions positives singulières associées à l'opérateur de Hardy–Sobolev]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 153-158.

Dans cette Note, nous présentons une classification complète des singularités de solutions positives de l'équation Δu+μ|x|2u=h(u) dans Ω{0}, où Ω est un domaine borné de RN, N3, 0Ω, et où 0<μ<(N2)24. Le cas μ=0 avec h(t)=tq, q>1 a été traité par Brezis et Véron.

In this Note, we present a complete classification of singularities of positive solutions of the equation Δu+μ|x|2u=h(u) in Ω{0}, where Ω is a bounded domain of RN, N3, 0Ω, and 0<μ<(N2)24. The case μ=0 with h(t)=tq, q>1 were treated by Brezis and Véron.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.12.018

Nirmalendu Chaudhuri 1 ; Florica C. Cîrstea 2

1 School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia
2 School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia
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Nirmalendu Chaudhuri; Florica C. Cîrstea. On trichotomy of positive singular solutions associated with the Hardy–Sobolev operator. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 153-158. doi : 10.1016/j.crma.2008.12.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.018/

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Cité par Sources :

This work were partially supported by an Australian Research Council Grant of Professors Neil Trudinger and Xu-Jia Wang.

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