Abstract
We study the existence and the asymptotic behavior of positive solutions for the parabolic equation
a
Δ
u
-
∂
∂
t
u
+
Vu
p
=
0
on
D
×
(
0
,
∞
)
, where
a
>
0
,
D
is a some unbounded domain in
R
n
,
n
⩾
3
and
V belongs to a new parabolic class
J
∞
of singular potentials generalizing the well-known parabolic Kato class at infinity
P
∞
introduced recently by Zhang. We also show that the choice of this class is essentially optimal.