Abstract
We introduce a novel definition of periodicity on arbitrary time scales, dependent on a strictly increasing and differentiable function. This removes the commonly used and restrictive assumption of a periodic time scale to define periodic functions. Our new definition furthermore allows for a wider class of functions to be studied using the theory of periodic systems. After providing crucial properties of these periodic functions, such as the translation invariance of integrals of periodic functions, we apply the concept of this new periodicity to linear dynamic equations. We provide necessary and sufficient conditions for a linear dynamic equation to have such a periodic solution and discuss its uniqueness.
Recommended Citation
M. Bohner et al., "A Unified Concept of Periodicity on Any Time Scale and Applications," Aims Mathematics, vol. 10, no. 9, pp. 21512 - 21532, AIMS Press, Jan 2025.
The definitive version is available at https://doi.org/10.3934/math.2025956
Department(s)
Mathematics and Statistics
Publication Status
Open Access
Keywords and Phrases
existence; global stability; linear dynamic equations; periodicity; time scales; uniqueness
International Standard Serial Number (ISSN)
2473-6988
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