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δ -Almost Periodic Functions and Applications to Dynamic Equations

Author

Listed:
  • Chao Wang

    (Department of Mathematics, Yunnan University, Kunming 650091, Yunnan, China
    Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA)

  • Ravi P. Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363-8202, USA
    Distinguished University Professor of Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA)

  • Donal O’Regan

    (School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland)

Abstract

In this paper, by employing matched spaces for time scales, we introduce a δ -almost periodic function and obtain some related properties. Also the hull equation for homogeneous dynamic equation is introduced and results of the existence are presented. In the sense of admitting exponential dichotomy for the homogeneous equation, the expression of a δ -almost periodic solution for a type of nonhomogeneous dynamic equation is obtained and the existence of δ -almost periodic solutions for new delay dynamic equations is considered. The results in this paper are valid for delay q -difference equations and delay dynamic equations whose delays may be completely separated from the time scale T .

Suggested Citation

  • Chao Wang & Ravi P. Agarwal & Donal O’Regan, 2019. "δ -Almost Periodic Functions and Applications to Dynamic Equations," Mathematics, MDPI, vol. 7(6), pages 1-27, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:525-:d:238443
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    References listed on IDEAS

    as
    1. Ahmad, Bashir & Ntouyas, Sotiris K. & Tariboon, Jessada & Alsaedi, Ahmed & Alsulami, Hamed H., 2016. "Impulsive fractional q-integro-difference equations with separated boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 199-213.
    2. Wang, Chao & Agarwal, Ravi P., 2015. "Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive Δ-dynamic system on time scales," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 271-292.
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