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The diffraction of a plane wave by a transversely inhomogeneous isotropicnonmagnetic linearly polarized dielectric layer filled with a Kerr-typenonlinear medium is considered. The analytical and numerical solutiontechniques are developed. The diffraction problem is reduced to a singularboundary value problem for a semilinear second-order ordinary differentialequation with a cubic nonlinearity and then to a cubic-nonlinear integralequation of the second kind and to a system of nonlinear operator equations ofthe second kind solved using iterations. Sufficient conditions of the uniquesolvability are obtained using the contraction principle.

Solvability of the boundary value problem associated with the wave diffraction by a layer filled with a Kerr-type nonlinear medium