Abstract
We are concerned with the following superlinear fourth-order equation
u
4
t
+
u
t
φ
t
,
−
u
t
=
0
,
t
∈
0
,
1
;
−
u
0
=
u
1
=
0
,
−
u
′
0
=
a
,
−
u
′
1
=
-
b
, where
a
,
−
b
are nonnegative constants such that
a
+
b
>
0
and
φ
t
,
−
s
is a nonnegative continuous function that is required to satisfy some appropriate conditions related to a class
K
satisfying suitable integrability condition. Our purpose is to prove the existence, uniqueness, and global behavior of a classical positive solution to the above problem by using a method based on estimates on the Green function and perturbation arguments.