Let
Ω
\Omega
be an open bounded domain in
R
N
(
N
≥
3
)
\mathbb {R}^N (N\geq 3)
with smooth boundary
∂
Ω
\partial \Omega
,
0
∈
Ω
0\!\in \!\Omega
. We are concerned with the asymptotic behavior of solutions for the elliptic problem:
(
∗
)
−
Δ
u
−
μ
u
|
x
|
2
=
f
(
x
,
u
)
,
u
∈
H
0
1
(
Ω
)
,
\begin{equation*} (*)\qquad \qquad \qquad \ -\Delta u-\frac {\mu u}{|x|^2}=f(x, u),\qquad \,\,u\in H^1_0(\Omega ),\qquad \qquad \qquad \qquad \ \ \end{equation*}
where
0
≤
μ
>
(
N
−
2
2
)
2
0\leq \mu >\big (\frac {N-2}{2}\big )^2
and
f
(
x
,
u
)
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.