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Advances in Continuous and Discrete Models

Theory and Modern Applications

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Solvability conditions for some difference operators

Advances in Difference Equations volume 2005, Article number: 514375 (2005) Cite this article

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.

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Authors and Affiliations

  1. Department of Mathematics, "Gh. Asachi" Technical University of Iasi, Iasi, 700506, Romania

    N C Apreutesei

  2. Laboratoire de Mathématiques Appliquées, Université Claude Bernard Lyon 1, Villeurbanne, 69622, France

    V A Volpert

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  1. N C Apreutesei
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  2. V A Volpert
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Correspondence to N C Apreutesei.

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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.

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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

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  • DOI: https://doi.org/10.1155/ADE.2005.1