Classification of singular solutions to the subcritical Lane-Emden equation in ${\mathbb{R}}^N\setminus \{0\}$

Abstract

We provide a classification result of positive solutions with a non-removable singularity at the origin to the subcritical Lane-Emden equation $-{\Delta }_{p}u=u^q$ in ${\mathbb{R}}^N\setminus \{0\}$, where $p\in (1,N)$, $q\in (p-1,p^{\ast }-1)$ and $u^{q-p+1}\in L^{\frac{N}{p}}({\mathbb{R}}^N\setminus B_R)$.