  The diffraction of a plane wave by a transversely inhomogeneous isotropic
nonmagnetic linearly polarized dielectric layer filled with a Kerr-type
nonlinear medium is considered. The analytical and numerical solution
techniques are developed. The diffraction problem is reduced to a singular
boundary value problem for a semilinear second-order ordinary differential
equation with a cubic nonlinearity and then to a cubic-nonlinear integral
equation of the second kind and to a system of nonlinear operator equations of
the second kind solved using iterations. Sufficient conditions of the unique
solvability are obtained using the contraction principle.
