Nonoscillatory Solutions for System of Delay Difference Equations on Time Scales

Abstract

In this paper, we consider certain system of delay difference equations
$$ \Delta{y_{1}(n)} = p(n)y_{2}(n)~~~~~~~ $$
$$ \Delta{y_{2}(n)} = -f(n,y_{1}(g(n)))$$
where $p(n)\in C[N_{0},R^{+}]$,~$yf(n,y)\geq{0}$,~$f\in{C[N_{0}\times{R},R]}$,~$y\sup\limits_{n\geq{n_{0}}}\mid f(n,y)\mid>0$ for any $y\neq0$,~$g(n)\in C[N_{0},R]$,~$g(n)\leq n$.