On a mixed value problem for a nonlinear partial differential equation containing a squared hyperbolic operator and nonlinear reflecting deviation

In this paper we consider the questions of one-valued solvability of the mixed problem for a nonlinear partial differential equation containing a squared hyperbolic operator and nonlinear reflecting deviation. Using the Fourier nonlinear method, we obtain a countable system of nonlinear integral equations. It is proved that the obtained series converges.