On a mixed value problem for nonlinear partial differential equation of the fourth order with reflecting deviation

In this paper we consider the questions of one value solvability of mixed problem for a nonlinear partial differential equation, consisting superposition of parabolic and elliptic operators in the left-hand side and reflecting deviation on the right-hand side of this equation. We accept the integral identity and by the Fourier method of separation variables we obtain the countable system of nonlinear integral equation with deviation. The one value solvability of this countable system of nonlinear integral equation we study by the method of successive approximations. The convergence of the Fourier series we prove on the base of the accepting in this work integral identity.