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

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.


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