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

TL;DR

This paper proves that positive solutions do not exist for certain nonlinear fractional elliptic inequalities in exterior domains, even under weak assumptions on the nonlinear term, extending known results to more general settings.

Contribution

It establishes new nonexistence results for positive solutions of fractional elliptic inequalities in exterior domains with minimal assumptions on the nonlinear term.

Findings

No positive solutions in exterior domains under weak nonlinear assumptions

Results apply even when considering the entire space

Extends nonexistence results to more general fractional elliptic inequalities

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.