Abstract
We prove the existence results in the setting of Orlicz spaces for the unilateral problem associated to the following equation,
A
u
+
g
(
x
,
u
,
∇
u
)
=
f
,
where
A
is a Leray–Lions operator acting from its domain
D
(
A
)
⊂
W
0
1
L
M
(
Ω
)
into its dual, while
g
(
x
,
u
,
∇
u
)
is a nonlinear term having a growth conditions with respect to
∇
u
and no growth with respect to
u
, but does not satisfy any sign condition. The right-hand side
f
belongs to
L
1
(
Ω
)
, and the obstacle is a measurable function.