An inhomogeneous p-laplacian equation with a Hardy potential

Abstract

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