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Behavior of positive solutions of a difference equation. (English) Zbl 1372.39005
Summary: In this paper we deal with the difference equation $y_{n+1}\frac{ay_{n-1}}{by_ny_{n-1}+cy_{n-1}y_{n-2}+d},\, n\in\mathbb{N}_0,$ where the coefficients $$a$$, $$b$$, $$c$$, $$d$$ are positive real numbers and the initial conditions $$y_2$$, $$y_1$$, $$y_0$$ are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.

##### MSC:
 39A10 Additive difference equations 39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type 39A23 Periodic solutions of difference equations
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