Abstract
We will be concerned with the existence result of a degenerate elliptic unilateral problem of the form
A
u
+
H
(
x
,
u
,
∇
u
)
=
f
, where
A
is a Leray-Lions operator from
W
1
,
p
(
Ω
,
w
)
into its dual. On the nonlinear lower-order term
H
(
x
,
u
,
∇
u
)
, we assume that it is a Carathéodory function having natural growth with respect to
|
∇
u
|
, but without assuming the sign condition. The right-hand side
f
belongs to
L
1
(
Ω
)
.