文档介绍:应 用 数 学
MATHEMATICA APPLICATA
2022, 35(3): 708-715
Existence and Uniqueness Theorems of
Almost Periodic Soluthe aid of the shift operators δ±, we studied almost periodicity in shifts
δ± on time scales, and give three definitions, that is, almost periodic time scale in shifts δ±,
almost periodic function in shifts δ± and ∆-almost periodic function in shifts δ±.
The purpose of this paper is to study the existence and uniqueness theorems of almost
periodic solution in shifts δ± of some nonlinear and linear dynamic equations on time scales,
and the specific expressions of almost periodic solutions in shifts δ± on finite and infinite
intervals will be given, respectively. Furthermore, we applying the obtained results to study
the existence of almost periodic solution in shifts δ± of a perturbed dynamic equation with
small positive parameters.
∗ Received date: 2021-09-08
Foundation item: Supported by the National Natural Science Foundation of China (11801012) and
the Key Scientific Research Project of Colleges and Universities of Henan Province (21A110001)
Biography: HU Meng, male, Han, Shandong, associate professor, major in differential . 3 HU Meng, et al.:Almost periodic solution in shifts δ on time scales 709
Consider the following dynamic equations on time scales
x∆(t) = A(t)x(t) + f(t, x(t))