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 $x=0$.
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