Propagation of TM waves in a shielded dielectric waveguide filled with nonlinear anisotropic medium

An eigenvalue problem that describes propagation of TM waves in a shielded dielectric layer filled with nonlinear anisotropic medium is studied. The non-linearity is of Kerr type and is characterized by two non-negative parameters α and β. It is proved that the considered problem has infinitely many eigenvalues for α > 0 and β ≥ 0 and only a finite number of eigenvalues if α = 0 and β > 0.