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Asymptotics and oscillation of nth-order nonlinear dynamic equations on time scales

Author

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  • Zhang, Shao-Yan
  • Wang, Qi-Ru
  • Kong, Qingkai

Abstract

This paper is concerned with nth-order nonlinear dynamic equations on time scales of the form (r(t)Φγ(xΔn−1(t)))Δ+∑i=0kqi(t)Φαi(x(δi(t)))=0with n ≥ 2. By discussing the signs of ith-order derivatives of eventually positive solutions for i=1,…,n−1, and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation. Our results extend many existing results in the literature.

Suggested Citation

  • Zhang, Shao-Yan & Wang, Qi-Ru & Kong, Qingkai, 2016. "Asymptotics and oscillation of nth-order nonlinear dynamic equations on time scales," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 324-334.
    • Handle: RePEc:eee:apmaco:v:275:y:2016:i:c:p:324-334
    DOI: 10.1016/j.amc.2015.11.084
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    Cited by:

    1. Yongkun Li & Xiaofang Meng, 2017. "Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales," Complexity, Hindawi, vol. 2017, pages 1-15, December.

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