School of Science
Xihua University
Chengdu 610039, Sichuan, China
email: zhengfengxiade@163.com
Department of Mathematics
Sichuan University
Chengdu 610064
Sichuan, China
email: hoxuli@scu.edu.cn
Feng-Xia Zheng, Hong-Xu Li
Abstract:
In this article, we generalize the concept of Stepanov-like almost
automorphic functions on time scales and present some properties including the
composition theorem. Based on it, some results on the existence and uniqueness of
almost automorphic solution to non-autonomous dynamic equations with Stepanov-like
almost automorphic forcing terms on time scales are established. In our results,
we do not need to assume the uniform Lipschitz condition of the nonlinear forcing
term and do not need to assume that the Green's function is Bi-automorphic directly.
Finally, an application to Lasota-Wazewska model on time scales is provided.
Submitted April 8, 2025. Published August 27, 2025.
Math Subject Classifications: 34C27, 34N05, 43A60.
Key Words: Non-autonomous dynamic equations; almost automorphic solutions; Stepanov-like almost automorphic; time scales.
DOI: 10.58997/ejde.2025.87
Show me the PDF file (445 KB), TEX file for this article.
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Feng-Xia Zheng School of Science Xihua University Chengdu 610039, Sichuan, China email: zhengfengxiade@163.com |
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Hong-Xu Li Department of Mathematics Sichuan University Chengdu 610064 Sichuan, China email: hoxuli@scu.edu.cn |
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