Abstract
We will consider the higher order functional dynamic equations with mixed nonlinearities of the formxnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scaleT, wheren≥2,xi(t)≔ri(t)ϕαixi-1Δ(t), i=1,…,n-1, with x0=x, ϕβ(u)≔uβsgnu, andα[i,j]≔αi⋯αj. The functionφi:T→Tis a rd-continuous function such thatlimt→∞φi(t)=∞forj=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.
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