A note on the classification of positive solutions to the critical p-Laplace equation in ${\mathbb{R}}^n$

Abstract

In this note, we obtain a classification result for positive solutions to the critical p-Laplace equation in ${\mathbb{R}}^n$ with $n\ge 4$ and $p>p_n$ for some number $p_n\in \left(\frac{n}{3},\frac{n+1}{3}\right)$ such that $p_n\sim \frac{n}{3}+\frac{1}{n}$, which slightly improves upon a similar result recently obtained by Ou under the condition $p\ge \frac{n+1}{3}$.

Final version to appear in Advanced Nonlinear Studies