An elliptic problem with critical exponent and positive Hardy potential

Abstract

We give the existence result and the vanishing order of the solution in $0$ for the following equation: $-\Delta u\left(x\right)+\left(\mu /{\left|x\right|}^2\right)u\left(x\right)=\lambda u\left(x\right)+u^{2*-1}\left(x\right)$, where $x\in B_1$, $\mu >0$, and the potential $\mu /{\left|x\right|}^2-\lambda$ is positive in $B_1$.