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

Abstract

We derive monotonicity formulae for solutions of the fractional Hénon-Lane-Emden equation \begin{equation*} (-Δ)^{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.

19 pages. To appear in Communications in Contemporary Mathematics. arXiv admin note: substantial text overlap with arXiv:1410.5400