An inhomogeneous p-laplacian equation with a Hardy potential

In this work we study the existence and regularity of solutions to the following equation: $$-{\mathrm{\Delta }}_{p}u+g(x)u=\frac{\lambda }{\mathrm{\mid }x{\mathrm{\mid }}^p}\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u+f,$$ where $1<p<N$ and $f\in L^m$, where $m\ge 1$.