Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 63, No. 4, pp. 407-414 (2006)

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Oscillation of difference equations with variable coefficients

Ozkan Ocalan

Afyon Kocatepe University, Faculty of Science and Arts, Department of Mathematics,
ANS Campus, 03200, Afyon -- TURKEY
E-mail: ozkan@aku.edu.tr

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.

Full text of the article:

Electronic version published on: 7 Mar 2008.

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