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Almost Automorphic Solutions in the Sense of Besicovitch to Nonautonomous Semilinear Evolution Equations

Author

Listed:
  • Yu Fei

    (School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China)

  • Yongkun Li

    (Department of Mathematics, Yunnan University, Kunming 650091, China)

Abstract

In this paper, we study the existence of almost automorphic solutions in the sense of Besicovitch for a class of semilinear evolution equations. Firstly, we study some basic properties of almost automorphic functions in the sense of Besicovitch, including the composition theorem. Then, by using the Banach fixed point theorem, the existence of almost automorphic solutions in the sense of Besicovitch to the semilinear equation is obtained. Finally, we give an example of partial differential equations to illustrate the applicability of our results.

Suggested Citation

  • Yu Fei & Yongkun Li, 2022. "Almost Automorphic Solutions in the Sense of Besicovitch to Nonautonomous Semilinear Evolution Equations," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:435-:d:737839
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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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