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.