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Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales

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  • Yongkun Li
  • Chao Wang

Abstract

Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scale 𝕋 = ℝ or â„€, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.

Suggested Citation

  • Yongkun Li & Chao Wang, 2011. "Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:341520
    DOI: 10.1155/2011/341520
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    References listed on IDEAS

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    1. Yongkun Li & Tianwei Zhang, 2010. "On the Existence of Solutions for Impulsive Duffing Dynamic Equations on Time Scales with Dirichlet Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-27, September.
    2. Yongkun Li & Tianwei Zhang, 2010. "On the Existence of Solutions for Impulsive Duffing Dynamic Equations on Time Scales with Dirichlet Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. Martin Bohner & Allan Peterson, 2001. "Dynamic Equations on Time Scales," Springer Books, Springer, number 978-1-4612-0201-1, March.
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    Cited by:

    1. Yongkun Li & Bing Li, 2015. "Almost Periodic Time Scales and Almost Periodic Functions on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2015(1).
    2. Yongkun Li & Li Yang, 2013. "Almost Periodic Solutions for Neutral‐Type BAM Neural Networks with Delays on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Chao Wang & Ravi P. Agarwal, 2014. "A Further Study of Almost Periodic Time Scales with Some Notes and Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Wenquan Wu, 2014. "Existence and Uniqueness of Globally Attractive Positive Almost Periodic Solution in a Predator‐Prey Dynamic System with Beddington‐DeAngelis Functional Response," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Yongkun Li & Chao Wang, 2012. "Almost Periodic Solutions to Dynamic Equations on Time Scales and Applications," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    6. Li Yang & Yongkun Li, 2014. "Existence and Global Exponential Stability of Almost Periodic Solutions for a Class of Delay Duffing Equations on Time Scales," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Li Yang & Yongkun Li & Wanqin Wu, 2014. "Cn‐Almost Periodic Functions and an Application to a Lasota‐Wazewska Model on Time Scales," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).

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