  A nonlinear electromagnetic scattering problem is studied in the presence of
bound states in the radiation continuum. It is shown that the solution is not
analytic in the nonlinear susceptibility and the conventional perturbation
theory fails. A non-perturbative approach is proposed and applied to the system
of two parallel periodic arrays of dielectric cylinders with a second order
nonlinear susceptibility. This scattering system is known to have bound states
in the radiation continuum. In particular, it is demonstrated that, for a wide
range of values of the nonlinear susceptibility, the conversion rate of the
incident fundamental harmonic into the second one can be as high as 40% when
the distance between the arrays is as low as a half of the incident radiation
wavelength. The effect is solely attributed to the presence of bound states in
the radiation continuum.
