Bulletin of the
Korean Mathematical Society BKMS

In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form $$\nabla_{\alpha}\left[x\left(t\right)-r\left(t\right)x\left(t-\kappa\right)\right]+p\left(t\right)x\left(t-\tau\right)-q\left(t\right)x\left(t-\sigma\right)=0,\quad t\geq t_{0},$$ where $t_{0}\in\mathbb{R}$, $t$ varies in the real interval $\left[t_{0},\infty\right)$, $\alpha>0$, $\kappa,\tau,\sigma\geq0$, $r\in C\left(\left[t_{0}-\alpha,\infty\right),\mathbb{R}^{+}\right)$, $p,q\in C\left(\left[t_{0},\infty\right),\mathbb{R}^{+}\right)$ and $\nabla_{\alpha}x\left(t\right)=x\left(t\right)-x\left(t-\alpha\right)$ for $t\geq t_{0}$.

Keywords: continuous variable, neutral difference equations, oscillation, positive and negative coefficients

MSC numbers: 39A10