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

Lalli, B. S.; Zhang, B. G.

J. Aust. Math. Soc., Ser. B 34, No. 2, 245-256 (1992).

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.

Reviewer: B.M.Agrawal (Lashkar-Gwalior)

MSC:

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

Keywords:

comparison theorems; neutral difference equation; oscillatory; oscillation; nonlinear