On the fractional Lane-Emden equation

Abstract

We classify solutions of finite Morse index of the fractional Lane-Emden equation \[ ( − Δ ) s u = | u | p − 1 u in  R n . (-\Delta )^{s} u = \vert u\vert ^{p-1} u\;\; \text {in $\mathbb {R}^n$.} \]