Existence of The Asymptotically Periodic Solution to the System of Nonlinear Neutral Difference Equations

Schmeidel, Ewa; Zdanowicz, MAŁgorzata

doi:10.2478/tmmp-2021-0025

Abstract

The system of nonlinear neutral difference equations with delays in the form ${\begin{cases} Δ (y_{i} (n) + p_{i} (n) y_{i} (n - τ_{i})) = a_{i} (n) f_{i} (y_{i + 1} (n)) + g_{i} (n), \\ Δ (y_{m} (n) + p_{m} (n) y_{m} (n - τ_{m})) = a_{m} (n) f_{m} (y_{1} (n)) + g_{m} (n), \end{cases}$ \[\left\{ \begin{array}{l} \Delta ({y_i}(n) + {p_i}(n){y_i}(n - {\tau _i})) = {a_i}(n){f_i}({y_{i + 1}}(n)) + {g_i}(n),\\ \Delta ({y_m}(n) + {p_m}(n){y_m}(n - {\tau _m})) = {a_m}(n){f_m}({y_1}(n)) + {g_m}(n), \end{array} \right.\] 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.

References

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Existence of The Asymptotically Periodic Solution to the System of Nonlinear Neutral Difference Equations

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