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On unstable neutral difference equations with “maxima”. (English) Zbl 1141.39002
The existence and asymptotic properties of nonoscillatory solutions are studied for the neutral type difference equation $$\Delta (x_n-p x_{n-\tau })=q_n \max_{s\in [n-\sigma ,n]}x_s$$, $$n=0,1,2,\dots$$, where $$p\in \mathbb R$$, $$\tau$$ is a positive integer, $$\sigma$$ is a nonnegative integer, $$\{q_n\}_0^\infty$$ is a nonnegative real sequence. Some oscillation results are also obtained.