On finite Morse index solutions of higher order fractional Lane-Emden equations

We classify finite Morse index solutions of the fractional Lane-Emden equation $(-\mathrm{\Delta }{)}^{s}u=\mathrm{\mid }u{\mathrm{\mid }}^{p-1}u{\mathbb{R}}^n$ for $1<s<2$. For the local case, $s=1$ and $s=2$ this classification was done by Farina in [10] and Davila, Dupaigne, Wang and Wei in [8], respectively. Moreover, for the nonlocal case, $0<s<1$, finite Morse index solutions are classified by Davila, Dupaigne and Wei in [7].