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Asymptotic properties of solutions of nonlinear second order neutral delay difference equations. (English) Zbl 0820.39005

The authors investigate the asymptotic properties of nonoscillatory solutions of a second order nonlinear neutral delay difference equation \[ \Delta^ 2 [y_{n - 1} + p_{n - 1} y_{n - 1 - k}] + q_ n f(y_{n - l}) = 0, \] where \(\Delta y_ n = y_{n + 1} - y_ n\), \(k,l \in \mathbb{N} = \{0,1, \dots\}\), and \(\{p_ n\}\) and \(\{q_ n\}\) are sequences of real numbers. Some sufficient conditions are also given to ensure that all solutions are oscillatory.

MSC:

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