Mixed value problem for nonlinear integro-differential equation with parabolic operator of higher power

We study the questions of one-valued solvability of mixed value problem for nonlinear integro-differential equation, consisting a parabolic operator of higher power. By the aid of Fourier series of separation variables the considering problem we can reduce to study the countable system of nonlinear integral equations, one-valued solvability of which will be proved by the method of successive approximations. The convergence of Fourier series will be studied by means of integral identity.