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

Abstract

In this note, we obtain a classification result for positive solutions to the critical p-Laplace equation in Rn ${\mathbb{R}}^{n}$ with n ≥ 4 and p > p n for some number pn∈n3,n+13 ${p}_{n}\in \left(\frac{n}{3},\frac{n+1}{3}\right)$ such that pn∼n3+1n ${p}_{n}\sim \frac{n}{3}+\frac{1}{n}$ , 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+13 $p\ge \frac{n+1}{3}$ .

Keywords

• classification of solutions
• p-laplace operator
• critical sobolev exponent
• 35j92
• 35b33