Uniform bound and a non-existence result for Lichnerowicz equation in the whole n-space

Abstract

In this Note, we give a uniform bound and a non-existence result for positive solutions to the Lichnerowicz equation in R n . In particular, we show that positive smooth solutions to: Δ u + f ( u ) = 0 , u > 0 , in R n where f ( u ) = u − p − 1 − u p − 1 , are uniformly bounded. To cite this article: L. Ma, X. Xu, C. R. Acad. Sci. Paris, Ser. I 347 (2009).