Bochner definition of Stepanov-like almost automorphic functions on time scales and an application to cellular neural networks with delays

Advances in Difference Equations

article

Zhang, Li-Li¹  Yang, Xu-Dong¹ 

[1] Department of Mathematics and Physics, Shijiazhuang Tiedao University

关键词: Time scale;    Bochner-like transform;    Stepanov-like almost automorphic function;    Dynamic equation;    Cellular neural networks;   

DOI  :  10.1186/s13662-021-03242-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

The definition of Stepanov-like almost automorphic functions on time scales had been proposed in the literature, but at least one result was incorrect, which involved Bochner transform. In our work, we give the Bochner definition of Stepanov-like almost automorphic functions on time scales, and prove that a function is Stepanov-like almost automorphic if and only if it satisfies Bochner definition of Stepanov-like almost automorphic function on time scales. The Bochner definition of Stepanov-like almost automorphic functions on time scales corrects the faulty result, and perfects the definition of Stepanov-like almost automorphic functions. As applications, we discuss the almost automorphy of a certain dynamic equation and some cellular neural networks with delays on time scales.

【 授权许可】

CC BY