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Zbl 0890.39019
Agarwal, R.P.; Thandapani, E.; Wong, P.J.Y.
Oscillations of higher-order neutral difference equations. (English)
[J] Appl. Math. Lett. 10, No.1, 71-78 (1997). ISSN 0893-9659

The authors investigate the oscillatory behavior of the solutions of an order $m$ nonlinear neutral difference equation of the form $$\Delta^m(y_n+p_ny_{n-k})+q_nf(y_{n-l})=0,\quad n\in\bbfN=\{0,1,\ldots\},$$ where $\Delta$ is the usual forward difference operator defined by $\Delta y_n=y_{n+1}-y_n$, $k$, $l$ are nonnegative integers, $\{p_n\}$, $\{q_n\}$ are real sequences with $q_n\ge 0$, $n\in\bbfN$, and $f:\bbfR\to\bbfR$ is continuous with $uf(u)>0$, for all $u\ne 0$. Some sufficient conditions are given which ensure that all solutions of the above equation are oscillatory.
[A.D.Mednykh (Novosibirsk)]

MSC 2000:: *39A12 Discrete version of topics in analysis
39A10 Difference equations

Keywords: nonlinear neutral difference equation; oscillatory solutions

Cited in: Zbl 1260.39018 Zbl 0970.39009

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