On the existence of a countable set of eigenvalues in the problem of TE-waves propagation in a circular cylindrical nonlinear waveguide

Background. The paper is devoted to a nonlinear eigenvalue problem arising in the theory of waveguides. The main goal is to prove the existence of propagation constants. Materials and methods. The original problem is reduced to a nonlinear eigenvalue problem for the Hammerstein integral operator. Thus the Weinberg theory can be applied to study the eigenvalue problem. Results. The study proves the existence of a discrete countable set of isolated eigenvalues. Conclusions. The method based on the Weinberg theory can be applied to study similar problems.