On stable solutions of the fractional Henon-Lane-Emden equation

We derive monotonicity formulae for solutions of the fractional H'{e}non-Lane-Emden equation \begin{equation*} (-\Delta)^{s} u=|x|^a |u|^{p-1} u \ \ \ $\text{in }$ \ \ $\mathbb{R}$^n, \end{equation*} when $0<s<2$, $a>0$ and $p>1$. Then, we apply these formulae to classify stable solutions of the above equation.