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Oscillatory and asymptotic behavior of solutions of nonlinear neutral-type difference equations. (English) Zbl 0890.39018
The authors investigate the oscillatory behavior of the solutions of an order \(m\) nonlinear neutral delay difference equation of the form \[ \Delta^m[y_{n-m+1}+p_{n-m+1}y_{n-m+1-k}]+\delta F(n,y_{n-l})=0. \] Two cases are considered: the first when \(\{p_n\}\) is allowed to oscillate about the bifurcation value \(-1\) and the second when the sequence \(\{p_n\}\) has arbitrary large zeros. Some illustrating examples are given and suggestions for further research are indicated.

MSC:
39A12 Discrete version of topics in analysis
39A10 Additive difference equations
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