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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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