Comptes Rendus
Differential Geometry/Mathematical Physics
Uniform bound and a non-existence result for Lichnerowicz equation in the whole n-space
[Une estimation uniforme et un résultat de non-existence pour l'équation de Lichnerowicz sur n-espace]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 805-808.

Dans cette Note, nous donnons une estimation uniforme et un résultat de non-existence pour les solutions positives de l'équation de Lichnerowicz sur Rn. En particulier, nous montrons que les solutions positives régulières de :

Δu+f(u)=0,u>0,dans Rn
f(u)=up1up1,
sont bornées.

In this Note, we give a uniform bound and a non-existence result for positive solutions to the Lichnerowicz equation in Rn. In particular, we show that positive smooth solutions to:

Δu+f(u)=0,u>0,in Rn
where
f(u)=up1up1,
are uniformly bounded.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.04.017

Li Ma 1 ; Xingwang Xu 2

1 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
2 Mathematics Department, The National University of Singapore, 10, Kent Ridge Crescent, Singapore 119260
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Li Ma; Xingwang Xu. Uniform bound and a non-existence result for Lichnerowicz equation in the whole n-space. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 805-808. doi : 10.1016/j.crma.2009.04.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.017/

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Cité par Sources :

The research is partially supported by the National Natural Science Foundation of China 10631020 and SRFDP 20060003002.

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