Existence of solutions to nonlocal elliptic equations with discontinuous terms

In this article, we study the existence of nonnegative solutions for the elliptic partial differential equation $$displaylines{ -[M(|u|^{p}_{1,p})]^{1,p}Delta_{p}u = f(x,u) quadhbox{in } Omega , cr u = 0 quadhbox{on } partialOmega , }$$ where $Omega subset mathbb{R}^N$ is a bounded smooth domain, $f:overline{Omega} imes mathbb{R}^+ o mathbb{R}$ is a discontinuous nonlinear function.