ON THE EXISTENCE OF NONLINEARIZABLE SOLUTIONS IN A NONCLASSICAL TWO-PARAMETER NONLINEAR BOUNDARY VALUE PROBLEM

Abstract

A nonlinear eigenvalue problem for a system of three equations with boundary conditions of the first kind, describing the propagation of electromagnetic waves in a plane nonlinear waveguide, is considered. This problem is two-parameter problem with one spectral parameter and a second parameter arising from an additional condition. This condition connects the constants of integration that arise when finding the first integrals of the system. The existence of nonlinearizable solutions to the problem is proven.