Abstract
AbstractFourth order problems with the differential equation $$y^{(4)}-(gy')'=\lambda ^2y$$
y
(
4
)
-
(
g
y
′
)
′
=
λ
2
y
, where $$g\in C^1[0,a]$$
g
∈
C
1
[
0
,
a
]
and $$a>0$$
a
>
0
, occur in engineering on stability of elastic rods. They occur as well in aeronautics to describe the stability of a flexible missile. Fourth order Birkhoff regular problems with the differential equation $$y^{(4)}-(gy')'=\lambda ^2y$$
y
(
4
)
-
(
g
y
′
)
′
=
λ
2
y
and eigenvalue dependent boundary conditions are considered. These problems have quadratic operator representations with non-self-adjoint operators. The first four terms of the asymptotics of the eigenvalues of the problems as well as those of the eigenvalues of the problem describing the stability of a flexible missile are evaluated explicitly.
Publisher
Springer Science and Business Media LLC