Oscillation criteria for two dimensional linear neutral delay difference systems
Arun Kumar Tripathy
Received April 17, 2021. Published online August 29, 2022.
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