Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 87, pp. 1-18.

Title: Almost automorphic solutions to non-autonomous dynamic equations with Stepanov-like almost automorphic forcing terms on time scales

Authors: Feng-Xia Zheng (Xihua Univ., Chengdu, Sichuan, China)
         Hong-Xu Li (Xihua Univ., Chengdu, Sichuan, China)

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.