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

Abstract

Abstract In this note, we obtain a classification result for positive solutions to the critical p-Laplace equation in R n ${\mathbb{R}}^{n}$ with n ≥ 4 and p > p n for some number p n ∈ n 3 , n + 1 3 ${p}_{n}\in \left(\frac{n}{3},\frac{n+1}{3}\right)$ such that p n ∼ n 3 + 1 n ${p}_{n}\sim \frac{n}{3}+\frac{1}{n}$ , which improves upon a similar result obtained by Ou (“On the classification of entire solutions to the critical p-Laplace equation,” 2022, arXiv:2210.05141) under the condition p ≥ n + 1 3 $p\ge \frac{n+1}{3}$ .