We classify finite Morse index solutions of the fractional Lane-Emden
equation (−Δ)su=∣u∣p−1u   Rn 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].Comment: To appear in American Journal of Math. 19 page