Abstract
AbstractThe aim of this paper is to consider a fully cantilever beam equation with one end fixed and the other connected to a resilient supporting device, that is,
$$ \textstyle\begin{cases} u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)), \quad t\in [0,1], \\ u(0)=u'(0)=0, \\ u''(1)=0,\qquad u'''(1)=g(u(1)), \end{cases} $$
{
u
(
4
)
(
t
)
=
f
(
t
,
u
(
t
)
,
u
′
(
t
)
,
u
″
(
t
)
,
u
‴
(
t
)
)
,
t
∈
[
0
,
1
]
,
u
(
0
)
=
u
′
(
0
)
=
0
,
u
″
(
1
)
=
0
,
u
‴
(
1
)
=
g
(
u
(
1
)
)
,
where $f:[0,1]\times \mathbb{R}^{4}\rightarrow \mathbb{R}$
f
:
[
0
,
1
]
×
R
4
→
R
, $g: \mathbb{R}\rightarrow \mathbb{R}$
g
:
R
→
R
are continuous functions. Under the assumption of monotonicity, two existence results for solutions are acquired with the monotone iterative technique and the auxiliary truncated function method.
Funder
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Cited by
4 articles.
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