A Liouville type theorem for fractional elliptic equation with exponential nonlinearity

In this paper, we are concerned with stable solutions to the fractional elliptic equation $$(-\mathrm{\Delta }{)}^{s}u=e^{u}in{\mathbb{R}}^N,$$ where $(-\mathrm{\Delta }{)}^s$ is the fractional Laplacian with $0<s<1$. We establish the nonexistence of stable solutions provided that $N<10s$. This result is optimal when $s\uparrow 1$.