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Almost Periodic Solutions of Differential Equations with Generalized Piecewise Constant Delay

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  • Kuo-Shou Chiu

    (Departamento de Matemática, Facultad de Ciencias Básicas, Universidad Metropolitana de Ciencias de la Educación, José Pedro Alessandri 774, Santiago 7760197, Chile)

Abstract

In this paper, we investigate differential equations with generalized piecewise constant delay, DEGPCD in short, and establish the existence and stability of a unique almost periodic solution that is exponentially stable. Our results are derived by utilizing the properties of the ( μ 1 , μ 2 ) -exponential dichotomy, Cauchy and Green matrices, a Gronwall-type inequality for DEGPCD, and the Banach fixed point theorem. We apply these findings to derive new criteria for the existence, uniqueness, and convergence dynamics of almost periodic solutions in both the linear inhomogeneous and quasilinear DEGPCD systems through the ( μ 1 , μ 2 ) -exponential dichotomy for difference equations. These results are novel and serve to recover, extend, and improve upon recent research.

Suggested Citation

  • Kuo-Shou Chiu, 2024. "Almost Periodic Solutions of Differential Equations with Generalized Piecewise Constant Delay," Mathematics, MDPI, vol. 12(22), pages 1-32, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3528-:d:1519124
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    References listed on IDEAS

    as
    1. Chiu, Kuo-Shou & Li, Tongxing, 2022. "New stability results for bidirectional associative memory neural networks model involving generalized piecewise constant delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 719-743.
    2. Yongkun Li, 2017. "Almost Automorphic Functions on the Quantum Time Scale and Applications," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-9, December.
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