## 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.

### MSC:

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

### Keywords:

difference equation
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