A P-function approach classifies all solutions to the weighted N-Liouville equation for N=2 and all α>-1, and for N≥3 when -1<α≤0, proving uniqueness of radial solutions in that range.
Takahashi, Nondegeneracy of the entire solution for the N-Laplace Liouville equation, Funkcial
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On the classification of solutions to a class of $N$-Liouville equations in $\mathbb{R}^N$
A P-function approach classifies all solutions to the weighted N-Liouville equation for N=2 and all α>-1, and for N≥3 when -1<α≤0, proving uniqueness of radial solutions in that range.