Approximation of a bounded solution of a linear difference equation on Z<sup class="a-plus-plus">2</sup> by solutions of corresponding boundary-value problems in a Banach space

Abstract

We study the problem of existence and uniqueness of solutions of boundary-value difference problems in a Banach space that correspond to a certain difference equation on Z². We prove a theorem on approximation of the unique bounded solution of the considered equation by solutions of the corresponding boundary-value problems.