# Positive solutions of anisotropic Yamabe--type equations in $R^n$

created by monti on 21 Oct 2007
modified on 27 Oct 2008

[BibTeX]

Published Paper

Inserted: 21 oct 2007
Last Updated: 27 oct 2008

Journal: Proc. AMS
Year: 2008

Abstract:

We study entire positive solutions to the partial differential equation in $R^n$ $$\Delta x u +(\alpha+1)2 x {2\alpha} \Deltay u = - x {2\alpha} u{\frac{n+2}{n-2}},$$ where $x\in R^2$, $y\in R^{n-2}$, $n\geq 3$ and $\alpha > 0$. We classify positive solutions with second order derivatives satisfying a suitable growth near the set $x=0$.