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Oscillatory and asymptotic behaviour of fourth order nonlinear neutral delay difference equations. (English) Zbl 1004.39005
The author considers the following nonlinear neutral delay difference equation $\Delta^2[r_n\Delta(y_n+p_ny_{n-k})]+f(n, y_{\sigma(n)})=0,$ where $$r_n>0, p_n>0$$ and $$\{\sigma(n)\}$$ is an increasing sequence of integers. Necessary and sufficient conditions are obtained for the existence of non-oscillatory solutions with a special asymptotic behaviour; also, sufficient conditions are obtained for all solutions to be oscillatory.

##### MSC:
 39A11 Stability of difference equations (MSC2000)