Skip to main content

Solvability conditions for some difference operators

Abstract

Infinite-dimensional difference operators are studied. Under the assumption that the coefficients of the operator have limits at infinity, limiting operators and associated polynomials are introduced. Under some specific conditions on the polynomials, the operator is Fredholm and has the zero index. Solvability conditions are obtained and the exponential behavior of solutions of the homogeneous equation at infinity is proved.

Author information

Affiliations

Authors

Corresponding author

Correspondence to N C Apreutesei.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Apreutesei, N.C., Volpert, V.A. Solvability conditions for some difference operators. Adv Differ Equ 2005, 514375 (2005). https://doi.org/10.1155/ADE.2005.1

Download citation