Advances in Difference Equations
Volume 2005 (2005), Issue 1, Pages 1-13
doi:10.1155/ADE.2005.1

Solvability conditions for some difference operators

N. C. Apreutesei1 and V. A. Volpert2

1Department of Mathematics, “Gh. Asachi” Technical University of Iasi, Iasi 700506, Romania
2Laboratoire de Mathématiques Appliquées, Université Claude Bernard Lyon 1, Villeurbanne 69622, France

Received 24 June 2004

Copyright © 2005 N. C. Apreutesei and V. A. Volpert. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.