Zinsou, Bertin2012-09-052012-09-052012-09-05http://hdl.handle.net/10539/11886We 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.enSpectral theory (Mathematics)Differential operators.Eigenvalues.Thesis