*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}} \Delta_{y} 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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