Piecewise Continuous Almost Automorphic Functions and Favard's Theorems for Impulsive Differential Equations In Honor of Russell Johnson

Liangping Qi Tianjin University of Finance and Economics Rong Yuan Beijing Normal University

Classical Analysis and ODEs mathscidoc:2103.05004

Journal of Dynamics and Differential Equations, 2020.8
We define piecewise continuous almost automorphic (p.c.a.a.) functions in the manners of Bochner, Bohr and Levitan, respectively, to describe almost automorphic motions in impulsive systems, and prove that with certain prefixed possible discontinuities they are equivalent to quasi-uniformly continuous Stepanov almost automorphic ones. Spatially almost automorphic sets on the line, which serve as suitable objects containing discontinuities of p.c.a.a. functions, are characterized in the manners of Bochner, Bohr and Levitan, respectively, and shown to be equivalent. Two Favard's theorems are established to illuminate the importance and convenience of p.c.a.a. functions in the study of almost periodically forced impulsive systems.
Piecewise continuous and Stepanov almost automorphic functions; spatially almost automorphic sets; Favard's theorems; impulsive differential equations.
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  • Published online: 07 August 2020
@inproceedings{liangping2020piecewise,
  title={Piecewise Continuous Almost Automorphic Functions and Favard's Theorems for Impulsive Differential Equations In Honor of Russell Johnson},
  author={Liangping Qi, and Rong Yuan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210328211050724600771},
  booktitle={Journal of Dynamics and Differential Equations},
  year={2020},
}
Liangping Qi, and Rong Yuan. Piecewise Continuous Almost Automorphic Functions and Favard's Theorems for Impulsive Differential Equations In Honor of Russell Johnson. 2020. In Journal of Dynamics and Differential Equations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210328211050724600771.
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