Study of the existence of supersolutions for nonlocal equations with gradient terms

Abstract

We study the existence of positive supersolutions of nonlocal equations $(-\Delta {)}^{s}u+|\nabla u{|}^q=\lambda f(u)$ in exterior domains where the datum $f$ can be comparade with $u^p$ near the origin. We prove that the existence or bounded supersolutions its depend of the values of $p$, $q$ and $s$.

23 pages, 6 figures