Nonlinear Multi-Parameter Eigenvalue Problems for Systems of Nonlinear Ordinary Differential Equations Arising in Electromagnetics

Abstract

We investigate a generalization of one-parameter eigenvalue problems arising in the theory of nonlinear waveguides to a more general nonlinear multiparameter eigenvalue problem for a nonlinear operator. Using an integral equation approach, we derive functional dispersion equations whose roots yield the desired eigenvalues. The existence and distribution of roots are verified.