Abstract
We present a general version of Massera's theorems for arbitrary discrete domains, based on a newly introduced definition for both linear and nonlinear equations. For scalar nonlinear equations, we identify sufficient conditions that ensure each µ-bounded solution approaches a periodic solution asymptotically. In the case of linear systems, we prove that the presence of a µ-bounded solution necessarily leads to a periodic solution. We also provide some examples to show the practical implications of our findings.
Recommended Citation
M. Bohner et al., "Massera’s Theorem On Arbitrary Discrete Time Domains," Mathematical Biosciences and Engineering, vol. 22, no. 7, pp. 1861 - 1874, AIMS Press, Jan 2025.
The definitive version is available at https://doi.org/10.3934/mbe.2025067
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
boundedness; isolated time scales; linear dynamic equations; nonlinear dynamic equations; periodicity
International Standard Serial Number (ISSN)
1551-0018; 1547-1063
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2025 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Jan 2025
Comments
Mathematisches Forschungsinstitut Oberwolfach, Grant None