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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Yongkun Li & Mei Huang & Bing Li, 2022. "Besicovitch Almost Periodic Solutions of Abstract Semi-Linear Differential Equations with Delay," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:639-:d:753122
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    References listed on IDEAS

    as
    1. Chiraz Jendoubi, 2021. "Dichotomy and μ‐pseudo almost automorphic solutions for delayed partial functional differential equations in admissible spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 294(2), pages 338-353, February.
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