Bull. Korean Math. Soc. 2010; 47(2): 401-409
Printed March 1, 2010
https://doi.org/10.4134/BKMS.2010.47.2.401
Copyright © The Korean Mathematical Society.
Ba\c{s}ak Karpuz and \"{O}zkan \"{O}calan
Faculty of Sciences and Arts and Faculty of Sciences and Arts
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
2003; 40(3): 489-501
2004; 41(4): 619-632
2005; 42(2): 245-256
2008; 45(1): 23-31
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