Oscillation of difference equations with variable coefficients

Ozkan Ocalan

Abstract: In this study, under some appropriate conditions over the real sequences $\{p_{n}\}$ and $\{q_{n}\}$ we give some sufficient conditions for the oscillation of all solutions of the difference equation
$$ x_{n+1}-x_{n}+\sum_{i=1}^{r}p_{in}x_{n-k_{i}}+q_{n}x_{n-m}=0, m\in\{...,-2,-1,0\} $$
where $k_{i}\in\Bbb{N}$ and $k_{i}\in\{...,-3,-2\}$ $(i=1,2,...,r)$, respectively.

Keywords: difference equation; oscillation.

Classification (MSC2000): 39A10.

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