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Zbl 0813.39004
Wyrwińska, Aleksandra
Oscillation criteria of a higher order linear difference equation. (English)
[J] Bull. Inst. Math., Acad. Sin. 22, No.3, 259-266 (1994). ISSN 0304-9825

Consider the following linear difference equation (1) $\Delta\sp m y(n) + (-1)\sp \nu a(n) y(r(n)) = 0$, $m \ge 2$, $\nu \in \{1,2\}$, where $\Delta\sp k y(n) = \sum\sp k\sb{i=0} (-1)\sp i {k \choose i} y(n+k-i)$, $k=0$, $1,\dots,m$, and $a:\bbfN \to \bbfR\sb +$, $r:\bbfN \to\bbfR$, $r(n) \le n$, $\lim\sb{n \to \infty} r(n) = \infty$. The author obtains sufficient conditions under which the solutions of the difference equation (1) are oscillatory. The obtained results are the discrete analogues of the results considered by {\it J. Werbowski} [Czech. Math. J. 36(111), 586-598 (1986; Zbl 0622.34074)].
[B.G.Pachpatte (Aurangabad)]

MSC 2000:: *39A10 Difference equations

Keywords: oscillation criteria; higher order linear difference equation; oscillatory solution

Citations: Zbl 0622.34074

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