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Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

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  • Taher S. Hassan
  • Said R. Grace

Abstract

We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above‐unbounded time scale T, where n ≥ 2, xi(t)≔ri(t)ϕαixi-1Δ(t), i=11,…,n-, with x[0] = x, ϕβ(u)≔|u|βsgn⁡u, and α[i, j]≔αi ⋯ αj. The function φi:T→T is a rd‐continuous function such that limt→∞φi(t) = ∞ for j = 0,1, …, N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

Suggested Citation

  • Taher S. Hassan & Said R. Grace, 2016. "Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:6847956
    DOI: 10.1155/2016/6847956
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    References listed on IDEAS

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    1. Sun, Yuangong & Hassan, Taher S., 2015. "Comparison criteria for odd order forced nonlinear functional neutral dynamic equations," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 387-395.
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