Formulation of some self-consistent tasks of radio electronics

The self-consistent problem of electromagnetism is defined as a closed mathematical cycle in which the primary sources of the electromagnetic field are corrected by the inverse effect of secondary sources arising from them as a result of the interaction of the radiation field with the surrounding medium. In a stationary state such a cycle is described by a homogeneous boundary value problem either on the differential, or integral, or integro-differential equations, that is, the eigenfunction and eigenvalue problem. Four most widespread variants of self-consistent boundary value problems are formulated.