Quasilinear elliptic problem with Hardy potential and singular term

Abstract

We consider the following quasilinear elliptic problem\begin{eqnarray*}-\Delta_pu =\lambda\frac{u^{p-1}}{|x|^p}+\frac{h}{u^\gamma}\quad in \quad\Omega,\end{eqnarray*}where $1 0$ and $h$ is a nonnegativemeasurable function with suitable hypotheses.The main goal of this work is to analyze the interaction betweenthe Hardy potential and the singular term $u^{-\gamma}$ in orderto get a solution for the largest possible class of the datum $h$.The regularity of the solution is also analyzed.