A nonlineair elliptic p.d.e. with singular potential

Abstract

In this paper, we prove the existence and the stability of the solution of the quasilineair elliptic equation
$-\Delta_{p}u-c\frac{u^{p-1}}{|x|^{p}}=u^{m}+tf\;\;\textrm{ in }\;\Omega$ where $0<c< c_{N,p}=(\frac{N-p}{p})^{p},\;1<p<N,\;m>p-1,\;t>0$ and $f$ is nonnegative measurable function.