%0 Journal Article
%T A Liouville theorem for non local elliptic equations
%A Louis Dupaigne
%A Yannick Sire
%J Mathematics
%D 2009
%I arXiv
%X We prove a Liouville-type theorem for bounded stable solutions $v \in C^2(\R^n)$ of elliptic equations of the type (-\Delta)^s v= f(v)\qquad {in $\R^n$,} where $s \in (0,1)$ {and $f$ is any nonnegative function}. The operator $(-\Delta)^s$ stands for the fractional Laplacian, a pseudo-differential operator of symbol $|\xi |^{2s}$.
%U http://arxiv.org/abs/0909.1650v1