Open Access

Solvability conditions for some difference operators

Advances in Difference Equations20052005:514375

DOI: 10.1155/ADE.2005.1

Received: 24 June 2004

Published: 14 March 2005

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.

Authors’ Affiliations

(1)
Department of Mathematics, "Gh. Asachi" Technical University of Iasi
(2)
Laboratoire de Mathématiques Appliquées, Université Claude Bernard Lyon 1

Copyright

© Apreutesei and Volpert 2005