Abstract
The boundary value problem of a fourth-order beam equation
u
4
=
λ
f
x
,
u
,
u
′
,
u
″
,
u
′
′
′
,
0
≤
x
≤
1
is investigated. We formulate a nonclassical cantilever beam problem with perturbed ends. By determining appropriate values of
λ
and estimates for perturbation measurements on the boundary data, we establish an existence theorem for the problem under integral boundary conditions
u
0
=
u
′
0
=
∫
0
1
p
x
u
x
d
x
,
u
″
1
=
u
′
′
′
1
=
∫
0
1
q
x
u
″
x
d
x
,
where
p
,
q
∈
L
1
0
,
1
,
and
f
is continuous on
0
,
1
×
0
,
∞
×
0
,
∞
×
−
∞
,
0
×
−
∞
,
0
.