The statement and solubility of boundary-value problems for Maxwell's equations in a cylinder

The paper deals with two problems of waveguide theory: the problem of radiation of electromagnetic waves in a regular waveguide with a filling variable in the cross-sections, and the problem of diffraction of an electromagnetic wave on a scatterer in a hollow waveguide. We consider radiation conditions and the solubility of the boundary-value problem for Maxwell's equations in a cylinder. We study several spectral problems connected with radiation conditions.