Unbounded increasing solutions of a system of difference equations with delays

Josef Diblík, Radoslav Chupáč and Miroslava Růžičková

Applied Mathematics and Computation, 2015, vol. 251, issue C, 489-498

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∈Z, pk,rk are integers, rk>pk⩾0, q is a positive integer, y=(y1,…,ys)T, y:{n0-r,n0-r+1,…}→Rs is an unknown discrete vector function, s⩾1 is an integer, 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⩾n0. The behavior of solutions of this system is discussed for 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.

Keywords: Unbounded solution; System of difference equations; Discrete delay; Exponential form (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:489-498

DOI: 10.1016/j.amc.2014.11.075

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