Existence of the asymptotically periodic solution to the system of nonlinear neutral difference equations

Year, pages: 2031, 149 - 162

The system of nonlinear neutral difference equations with delays in the form \[ \{\begin{array}{l} Δ \big(y_i(n)+p_i(n) y_i(n-τ_i)\big)=a_i(n) f_i(y_i+1(n))+g_i(n), Δ \big(y_m(n)+p_m(n) y_m(n-τ_m)\big)=a_m(n) f_m(y₁(n))+g_m(n), \end{array} . \] for $i=1,…,m-1$, $m≥ 2$, is studied. The sufficient conditions for the existence of an asymptotically periodic solution of the above system, are established. Here sequences $(p_i(n))$, $i=1,…,m$, are bounded away from -1. The presented results are illustrated by theoretical and numerical examples.

Schmeidel, E., Zdanowicz, M. 2031. Existence of the asymptotically periodic solution to the system of nonlinear neutral difference equations. In Tatra Mountains Mathematical Publications, vol. 79, no.2, pp. 149-162. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0025

Schmeidel, E., Zdanowicz, M. (2031). Existence of the asymptotically periodic solution to the system of nonlinear neutral difference equations. Tatra Mountains Mathematical Publications, 79(2), 149-162. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0025

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/