A.Yu. Sedakov

There are examined questions of definition and classification of boundary tasks describing waves of layer-like directing structures with thin resistive films. There is justified the correctness of surface current technique (SCT) different from PET by the use of discontinuous boundary conditions for magnetic field at resistive films location. It is proved that SCT does not violate classification rules of electrodynamic operators in that case too when all selected partial environment fields have actual ε and μ parameters. Satisfaction of the mentioned rules proves SCT correctness considering system completeness of boundary tasks solutions i.e. completeness of waves spectrum corresponding to the solutions. There are described the peculiarities of dispersion equations procedures of layer-like waveguides waves with resistive films. There are ex-amined the cases of homogeneous and semi-homogeneous boundary tasks. Under semi-homogeneous boundary task it is understood the task based on homogeneous Helmholtz equation with heterogeneous boundary conditions: impedance to shielded structures and nontrivial at infinity to open structures. There are examined existence conditions of branches connection of homogeneous and semi-homogeneous boundary tasks dispersion equations solutions.