Existence of solution for a system involving fractional Laplacians and a Radon measure

An existence of a nontrivial solution in some `weaker' sense of the following system of equations \begin{align*} (-\Delta)^{s}u+l(x)\phi u+w(x)|u|^{k-1}u&=\mu~\text{in}~\Omega\nonumber\\ (-\Delta)^{s}\phi&= l(x)u^2~\text{in}~\Omega\nonumber\\ u=\phi&=0 ~\text{in}~\mathbb{R}^N\setminus\Omega \end{align*} has been proved. Here \(s \in (0,1)\), \(l,w\) are bounded nonnegative functions in \(\Omega\), \(\mu\) is a Radon measure and \(k > 1\) belongs to a certain range.