Approximate solution of nonlinear discrete equations of convolution type

S. N. Askhabov

Contemporary Mathematics. Fundamental Directions, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, Tome 45 (2012), pp. 18-31

Résumé

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 $\ell_p$. Using the property of potentiality of the operators under consideration, in the case of space $\ell_2$ and in the case of a weighted space $\ell_p(\varrho)$ with a generic weight $\varrho$ 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.