Eigenvalues of two parameter polynomial operator pencils of waveguide type


Colakoglu N., HASANOV M., UZUN B. U.

INTEGRAL EQUATIONS AND OPERATOR THEORY, vol.56, no.3, pp.381-400, 2006 (SCI-Expanded) identifier identifier

Abstract

The spectral structure of two parameter unbounded operator pencils of waveguide type is studied. Theorems on discreteness of the spectrum for a fixed parameter are proved. Variational principles for real eigenvalues in some parts of the root zones are established. In the case of n = 1 (quadratic pencils) domains containing the spectrum are described (see Fig. 1-3). Conditions in the definition of the pencils of waveguide type arise naturally from physical problems and each of them has a physical meaning. In particular a connection between the energetic stability condition and a perturbation problem for the coefficients is given.