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Asymptotic Representation for Solutions of Difference Systems

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Asymptotic Integration of Differential and Difference Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2129))

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Abstract

In this chapter we first consider systems of linear difference equations

$$\displaystyle{ y(n + 1) = A(n)y(n),\qquad n \geq n_{0}, }$$
(3.1)

which are in what we call l 1-diagonal form

$$\displaystyle{ y(n + 1) = [\varLambda (n) + R(n)]y(n),\qquad n \geq n_{0} }$$
(3.2)

and establish results similar to those in Sects. 2.2–2.4. This includes discrete versions of Coppel’s theorem and Levinson’s fundamental theorem from Sect. 2.2 for l 1-diagonal systems, and some results for weak dichotomies.

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Authors and Affiliations

  1. Dept. of Mathematics and Computer Science, University of Puget Sound, Tacoma, WA, USA

    Sigrun Bodine

  2. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Donald A. Lutz

Authors
  1. Sigrun Bodine
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  2. Donald A. Lutz
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Bodine, S., Lutz, D.A. (2015). Asymptotic Representation for Solutions of Difference Systems. In: Asymptotic Integration of Differential and Difference Equations. Lecture Notes in Mathematics, vol 2129. Springer, Cham. https://doi.org/10.1007/978-3-319-18248-3_3

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