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Almost Automorphic Solutions to Nonlinear Difference Equations

Author

Listed:
  • Marko Kostić

    (Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia)

  • Halis Can Koyuncuoğlu

    (Department of Engineering Sciences, Izmir Katip Celebi University, 35620 Izmir, Turkey)

  • Vladimir E. Fedorov

    (Department of Mathematical Analysis, Mathematics Faculty, Chelyabinsk State University, Kashirin Brothers St. 129, Chelyabinsk 454001, Russia)

Abstract

In the present work, we concentrate on a certain class of nonlinear difference equations and propose sufficient conditions for the existence of their almost automorphic solutions. In our analysis, we invert an appropriate mapping and obtain the main existence outcomes by utilizing the contraction mapping principle. As the second objective of the manuscript, we reconsider one of the landmark results, namely the Bohr–Neugebauer theorem, in the qualitative theory of dynamical equations, and we investigate the relationship between the existence of almost automorphic solutions and the existence of solutions with a relatively compact range for the proposed difference equation type. Thus, we provide a discrete counterpart of the Bohr–Neugebauer theorem due to the almost automorphy notion under some technical conditions.

Suggested Citation

  • Marko Kostić & Halis Can Koyuncuoğlu & Vladimir E. Fedorov, 2023. "Almost Automorphic Solutions to Nonlinear Difference Equations," Mathematics, MDPI, vol. 11(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4824-:d:1290765
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    References listed on IDEAS

    as
    1. Nguyen Van Minh & Ha Binh Minh, 2004. "A Massera-type criterion for almost periodic solutions of higher-order delay or advance abstract functional differential equations," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-16, January.
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