Monotonicity results for quasilinear fractional systems in epigraphs

Abstract

We prove the monotonicity of positive solutions to the quasilinear fractional system

where $\Omega$ is a coercive or non-coercive epigraph, such as the halfspace ${\mathbb{R}}_{+}^n$, $0<s,t<1$ and $p,q\ge 2$. By combining a new decay at infinity principle with the direct method of moving planes, we improve recent works in the literature even in the case of a single equation.