Mathematical Theory of Surface Waves in an Inhomogeneous Waveguide

The problem on surface waves in an inhomogeneous metal-dielectric waveguide structure is reduced to a boundary value problem for the longitudinal components of the electromagnetic field in Sobolev spaces. We formulate the definition of solution using variational relation. The variational problem is reduced to the study of an operator function. We investigate properties of the operators of the operator function needed for the analysis of its spectral properties. We prove theorem of discrete spectrum.