Oscillation criteria for two dimensional linear neutral delay difference systems

Abstract

In this work, necessary and sufficient conditions for the oscillation of solutions of 2-dimensional linear neutral delay difference systems of the form \Delta\left[\matrix x(n)+p(n)x(n-m) y(n)+p(n)y(n-m) \right]= \left[\matrix a(n) & b(n) c(n) & d(n) \right]\left[\matrix x(n-\alpha) y(n-\beta) \right] are established, where $m>0$, $\alpha\geq0$, $\beta\geq0$ are integers and $a(n)$, $b(n)$, $c(n)$, $d(n)$, $p(n)$ are sequences of real numbers.

Keywords

• oscillation
• nonoscillation
• system of neutral equations
• krasnoselskii's fixed point theorem