Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order - Taher S. Hassan; Said R. Grace (Discrete Dynamics in Nature and Society)
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.