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Oscillation and comparison theorems for certain neutral difference equations. (English) Zbl 0759.39002

A nontrivial solution \(\{y_ n\}\) of the neutral difference equation, (1) \(\Delta(y_ n+cy_{n-m})+p_ ny_{n-k}=0\), \(n=0,1,2,\dots\), is said to be oscillatory if for every \(N>0\), \(\exists n\geq N\): \(y_ ny_{n+1}\leq 0\). By establishing a necessary and sufficient condition for the oscillation of (1), sufficient conditions for oscillation of neutral difference equations with mixed arguments and equations with nonlinear terms are obtained.

MSC:

39A10 Additive difference equations
39A11 Stability of difference equations (MSC2000)
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