Abstract
We discuss the existence of positive solutions of a nonlinear
n
th order boundary value problem
u
(
n
)
+
a
(
t
)
f
(
u
)
=
0
,
t
∈
(
0
,
1
)
u
(
0
)
=
0
,
u
′
(
0
)
=
0
,
…
,
u
(
n
−
2
)
(
0
)
=
0
,
α
u
(
η
)
=
u
(
1
)
,
where
0
<
η
<
1
,
0
<
α
η
n
−
1
<
1
. In particular, we establish the existence of at least one positive solution if
f
is either superlinear or sublinear by applying the fixed point theorem in cones due to Krasnoselkiǐ and Guo.