Asymptotic behavior of solutions to semilinear elliptic equations with Hardy potential

Let $\Omega$ be an open bounded domain in $\mathbb{R}^N (N\geq3)$ with smooth boundary $\partial\Omega$, $0\in\Omega$. We are concerned with the asymptotic behavior of solutions for the elliptic problem:

$(*)\qquad\qquad\qquad -\Delta u-\frac{\mu u}{\vert x\vert^2}=f(x, u),\qquad\,\,u\in H^1_0(\Omega),\qquad\qquad\qquad\qquad$

where $0\leq\mu<\big(\frac{N-2}{2}\big)^2$ and $f(x, u)$ satisfies suitable growth conditions. By Moser iteration, we characterize the asymptotic behavior of nontrivial solutions for problem $(*)$. In particular, we point out that the proof of Proposition 2.1 in Proc. Amer. Math. Soc. 132 (2004), 3225-3229, is wrong.