Multiparameter Eigenvalue Problems and Their Applications in Electrodynamics

A nonlinear n-parametric eigenvalue problem called the problem P is considered. In addition to n spectral parameters, the problem P depends on n2 numerical parameters; for zero values of these parameters, the problem splits into n linear problems Pi0,i=1,n¯. To the problem P, one can assign n nonlinear problems Pi, which, in particular, have solutions that are not related to the solutions of the problems Pi0. The problems Pi are treated in this work as “nonperturbed” problems. Using the properties of eigenvalues of the problems Pi, we prove the existence of eigenvalues of the problem P; some of these eigenvalues are not related to solutions of the problems Pi0. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.