Author:
Guo Yanping,Yang Fei,Liang Yongchun
Abstract
Abstract
In this article, by the fixed point theorem in a cone and the nonlocal fourth-order BVP's Green function, the existence of at least one positive solution for the nonlocal fourth-order boundary value problem with all order derivatives
u
(
4
)
(
t
)
+
A
u
″
(
t
)
=
λ
f
(
t
,
u
(
t
)
,
u
′
(
t
)
,
u
″
(
t
)
,
u
‴
(
t
)
)
,
0
<
t
<
1
,
u
(
0
)
=
u
(
1
)
=
∫
0
1
p
(
s
)
u
(
s
)
d
s
,
u
″
(
0
)
=
u
″
(
1
)
=
∫
0
1
q
(
s
)
u
″
(
s
)
d
s
is considered, where f is a nonnegative continuous function, λ > 0, 0 < A < π
2, p, q ∈ L[0, 1], p(s) ≥ 0, q(s) ≥ 0. The emphasis here is that f depends on all order derivatives.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Cited by
8 articles.
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