We consider on the interval [0; a], rstly fourth-order di erential operators with eigenvalue
parameter dependent boundary conditions and secondly a sixth-order di erential operator
with eigenvalue parameter dependent boundary conditions. We associate to each of these
problems a quadratic operator pencil with self-adjoint operators. We investigate the spectral
proprieties of these problems, the location of the eigenvalues and we explicitly derive the rst
four terms of the eigenvalue asymptotics.
