Approximate Solution of Nonlinear Discrete Equations of Convolution Type

By the method of potential monotone operators we prove global theorems on existence, uniqueness, and ways to find a solution for different classes of nonlinear discrete equations of convolution type with kernels of special form both in weighted and in weightless real spaces ? _p . Using the property of potentiality of the operators under consideration, in the case of space ? ₂ and in the case of a weighted space ? _p (?) with a generic weight ?, we prove that a discrete equation of convolution type with an odd power nonlinearity has a unique solution and it (the main result) can be found by gradient method.