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Dichotomy and μ‐pseudo almost automorphic solutions for delayed partial functional differential equations in admissible spaces

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  • Chiraz Jendoubi

Abstract

We prove the existence and uniqueness of μ‐pseudo almost automorphic solution for a delayed non‐autonomous partial functional differential equation in the exponential dichotomic case, where the nonlinear operator F satisfies the φ‐Lipschitz condition and φ belongs to some admissible spaces. We further prove the existence of an invariant stable manifold around the μ‐pseudo almost automorphic solution in that case. An application is given to illustrate our theory.

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  • 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.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:2:p:338-353
    DOI: 10.1002/mana.201800134
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    Cited by:

    1. 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.
    2. 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.

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