Article ID Journal Published Year Pages File Type
4627021 Applied Mathematics and Computation 2015 10 Pages PDF
Abstract

We consider a homogeneous system of difference equations with deviating arguments in the formΔy(n)=∑k=1qβk(n)[y(n-pk)-y(n-rk)],where n⩾n0,n0∈Zn⩾n0,n0∈Z, pk,rkpk,rk are integers, rk>pk⩾0rk>pk⩾0, q   is a positive integer, y=(y1,…,ys)Ty=(y1,…,ys)T, y:{n0-r,n0-r+1,…}→Rsy:{n0-r,n0-r+1,…}→Rs is an unknown discrete vector function, s⩾1s⩾1 is an integer, r=max{r1,…,rq},Δy(n)=y(n+1)-y(n)r=max{r1,…,rq},Δy(n)=y(n+1)-y(n), and βk(n)=(βijk(n))i,j=1s are real matrices such that βijk:{n0,n0+1,…}→[0,∞), and ∑k=1q∑j=1sβijk(n)>0 for each admissible i   and all n⩾n0n⩾n0. The behavior of solutions of this system is discussed for n→∞n→∞. The existence of unbounded increasing solutions in an exponential form is proved and estimates of solutions are given. The scalar case is discussed as well.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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