Abstract
Given a bounded open regular set
Ω
∈
R
4
,
x
1
,
x
2
,
…
,
x
m
∈
Ω
,
λ
,
ρ
>
0
,
γ
∈
(
0
,
1
)
, and
Q
λ
some nonlinear operator (which will be defined later), we prove that the problem
Δ
2
u
+
Q
λ
(
u
)
=
ρ
4
(
e
u
+
e
γ
u
)
has a positive weak solution in
Ω
with
u
=
Δ
u
=
0
on
∂Ω
, which is singular at each
x
i
as the parameters
λ
and
ρ
tend to 0.