Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

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=1,…,n-1,   with  x0=x,  ϕβ(u)≔uβsgn⁡u, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous functi...

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Bibliographic Details
Main Authors: Taher S. Hassan, Said R. Grace
Format: Article
Language:English
Published: Wiley 2016-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2016/6847956
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Summary: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=1,…,n-1,   with  x0=x,  ϕβ(u)≔uβsgn⁡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.
ISSN:1026-0226
1607-887X

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