Affiliation:
1. University of Arkansas at Little Rock
Abstract
Let
m
≥
2
and
a
,
b
,
c
>
0
. We consider the existence and uniqueness of solutions for the fourth order iterative boundary value problem,
x
(
4
)
(
t
)
=
−
f
(
t
,
x
(
t
)
,
x
[
2
]
(
t
)
,
…
,
x
[
m
]
(
t
)
)
,
−
a
≤
t
≤
a
where
x
[
2
]
(
t
)
=
x
(
x
(
t
)
)
and for
j
=
3
,
…
,
m
,
x
[
j
]
(
t
)
=
x
(
x
[
j
−
1
]
(
t
)
)
, with solutions satisfying one of the following sets of conjugate boundary conditions:
x
(
−
a
)
=
−
a
,
x
′
(
−
a
)
=
b
,
x
″
(
−
a
)
=
c
,
x
(
a
)
=
a
,
x
(
−
a
)
=
−
a
,
x
(
a
)
=
a
,
x
′
(
a
)
=
b
,
x
″
(
a
)
=
c
.
The main tool used is the Schauder fixed point theorem.