Existence of positive weak solutions for a nonlocal singular elliptic system

Abstract

Let $\Omega$ be a bounded domain in $\mathbb{R}^{n}$ with $C^{1, 1}$ boundary, and let $s\in\left(0, 1\right) $ be such that $s 0$ in $\Omega, $ $v>0$ in $\Omega, $ where $a$ and $b$ are nonnegative bounded measurable functions such that $\inf_{\Omega}a>0$ and $\inf_{\Omega}b>0.$ For the found weak solution $\left(u, v\right), $ the behavior of $u$ and $v$ near $\partial\Omega$ is also investigated.