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International Conference on Difference Equations and Applications

ICDEA 2017: Difference Equations, Discrete Dynamical Systems and Applications pp 273–283Cite as

Existence and Stability Properties of Almost Periodic Solutions in Discrete Almost Periodic Systems

Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 287)

Abstract

In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: \( x(n+1) = A(n)x(n) \) and \( x_{i}(n+1)=\sum _{j=1}^{m}a_{ij}(n)g_{j}(x_{j}(n)) \quad \text{ for } \quad 1 \le i \le m \), respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.

Keywords

  • Almost periodic solutions on \( \mathbf {Z^{+}} \)
  • Linear and nonlinear almost periodic discrete systems
  • Uniformly asymptotically stable
  • Diagonal dominance matrix condition

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Authors and Affiliations

  1. Department of Information Science, Okayama University of Science, 1-1 Ridai-cho, Okayama, 700-0005, Japan

    Yoshihiro Hamaya

Authors
  1. Yoshihiro Hamaya
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Correspondence to Yoshihiro Hamaya .

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Editors and Affiliations

  1. Department of Mathematics, Trinity University, San Antonio, TX, USA

    Prof. Dr. Saber Elaydi

  2. Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Klagenfurt, Austria

    Prof. Dr. Christian Pötzsche

  3. Department of Mathematics, West University of Timişoara, Timişoara, Romania

    Prof. Dr. Adina Luminiţa Sasu

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Hamaya, Y. (2019). Existence and Stability Properties of Almost Periodic Solutions in Discrete Almost Periodic Systems. In: Elaydi, S., Pötzsche, C., Sasu, A. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2017. Springer Proceedings in Mathematics & Statistics, vol 287. Springer, Cham. https://doi.org/10.1007/978-3-030-20016-9_11

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