Besicovitch Almost Periodic Solutions of Abstract Semi-Linear Differential Equations with Delay

Yongkun Li, Mei Huang and Bing Li
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Yongkun Li: Department of Mathematics, Yunnan University, Kunming 650091, China
Mei Huang: Department of Mathematics, Yunnan University, Kunming 650091, China
Bing Li: School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China

Mathematics, 2022, vol. 10, issue 4, 1-15

Abstract: In this paper, first, we give a definition of Besicovitch almost periodic functions by using the Bohr property and the Bochner property, respectively; study some basic properties of Besicovitch almost periodic functions, including composition theorem; and prove the equivalence of the Bohr definition and the Bochner definition. Then, using the contraction fixed point theorem, we study the existence and uniqueness of Besicovitch almost periodic solutions for a class of abstract semi-linear delay differential equations. Even if the equation we consider degenerates into ordinary differential equations, our result is new.

Keywords: Besicovitch almost periodic function; semi-linear differential equation; time delay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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