  Optimal estimates on the asymptotic behaviors of weak solutions both at the
origin and at the infinity are obtained to the following quasilinear elliptic
equations
\[-\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u=Q(x)|u|^{\frac{Np}{N-p}-2}u,\quad\,x\in
\mathbb{R}^{N},\] where $1<p<N, 0\leq\mu<\left({(N-p)}/{p}\right)^{p}$ and
$Q\in L^{\infty}(\mathbb{R}^{N})$.
