Real resonances in a waveguide with nonhomogeneous filling

Eigenvalues embedded in continuous spectra of spectral problems for acoustic and electromagnetic waveguides with filling have been considered. A criterion for the existence of an infinite sequence of eigenvalues for fillings of the insertion type has been given. In the case of fillings of the "simple insert" and "elbow" types, the eigenvalues have been found as roots of transcendental equations.