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 $-Δ_p u = u^q$ in $\mathbb{R}^N \setminus \{0\}$, where $p\in(1,N)$, $q\in (p-1,p^*-1)$ and $u^{q-p+1} \in L^{\frac{N}{p}}(\mathbb{R}^N \setminus B_R)$.