Spectral theory of self-adjoint higher order differential operators with eigenvalue parameter dependent boundary conditions
Date
2012-09-05
Authors
Zinsou, Bertin
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Abstract
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.