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Exact Asymptotic Behavior of the Solution of a Matrix Difference Equation

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Abstract

An asymptotic expansion of the solution of a nonhomogeneous matrix difference equation of general form is obtained. The case when there is no bound on the differences of the arguments is considered. The effect of the roots of the characteristic equation is taken into account. The asymptotic behavior of the remainder is established depending on the asymptotics of the free term of the equation.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russian Federation, 630090

    M. S. Sgibnev

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  1. M. S. Sgibnev
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Correspondence to M. S. Sgibnev.

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The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (Project No. 0314-2019-0005).

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Sgibnev, M.S. Exact Asymptotic Behavior of the Solution of a Matrix Difference Equation. J Dyn Diff Equat 34, 1173–1186 (2022). https://doi.org/10.1007/s10884-020-09923-7

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  • DOI: https://doi.org/10.1007/s10884-020-09923-7

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