Nonexistence of positive supersolutions for semilinear fractional elliptic equations in exterior domains

Abstract

This article is concerned with the nonexistence of positive solutions for nonlinear fractional elliptic inequalities in exterior domains of $\mathbb R^n$, $n\geq1$. We would like to highlight the fact that our results are new with very weak assumption on the nonlinear term appearing in the inequalities. The results are also novel in this generality even if the whole space is considered.