Oscillation properties for advanced difference equations. (English) Zbl 1224.39017

Öcalan, Özkan; Akin, Ömer

Novi Sad J. Math. 37, No. 1, 39-47 (2007).

The authors provide some sufficient conditions for the oscillation of every solution of the difference equation \(x_{n+1}-x_n+p_nx_{n-k}=0\), \(n=0,1,2,\dots\) whenever \(k\in\{\dots,-3,-2\}\) and \(p_n\leq0\), and also \(x_{n+1}-x_n+\sum_{i=1}^mp_{in}x_{n-k_i}=0\), \(n=0,1,2,\dots\) whenever \(k\in\{\dots,-3,-2,-1\}\) and \(p_{in}\leq0\) for \(i=1,2,\dots,m\). They also obtain some alternative results for the oscillation of all solutions of these equations.

Reviewer: Miloš Čanak (Beograd)

MSC:

39A21	Oscillation theory for difference equations
39A10	Additive difference equations

Keywords:

difference equation