Abstract
We establish the existence and uniqueness of a positive solution to the following fourth-order value problem:
u
(
4
)
(
x
)
=
a
(
x
)
u
σ
(
x
)
,
x
∈
(
0,1
)
with the boundary conditions
u
(
0
)
=
u
(
1
)
=
u
'
(
0
)
=
u
'
(
1
)
=
0
, where
σ
∈
(
-
1,1
)
and
a
is a nonnegative continuous function on (0, 1) that may be singular at
x
=
0
or
x
=
1
. We also give the global behavior of such a solution.