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Almost Automorphic Solutions to Nonlinear Difference Equations
Version 1
: Received: 3 November 2023 / Approved: 3 November 2023 / Online: 6 November 2023 (03:08:22 CET)
A peer-reviewed article of this Preprint also exists.
Kostić, M.; Koyuncuoğlu, C.; Fedorov, V.E. Almost Automorphic Solutions to Nonlinear Difference Equations. Mathematics 2023, 11, 4824. Kostić, M.; Koyuncuoğlu, C.; Fedorov, V.E. Almost Automorphic Solutions to Nonlinear Difference Equations. Mathematics 2023, 11, 4824.
Abstract
In this study, we focus on an abstract form of summation equations, which can be regarded
as a particular class of nonlinear difference equations. We investigate sufficient conditions for
the existence of discrete almost automorphic solutions by appealing to the fixed point theory and
establish a linkage between the existence of discrete almost automorphic solutions and the existence
of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we
propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference
equations.
Keywords
discrete almost automorphic; discrete bi-almost automorphic; fixed point; contraction; Bohr-Neugebauer
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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