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The dynamics of \(x_{n+1}= \frac {\alpha + \beta x_n}{A+Bx_n+Cx_{n-1}}\) facts and conjectures. (English) Zbl 1077.39004
The authors investigate the global character of the solutions of the equation in the title with nonnegative parameters and initial conditions such as the global attractivity, local and global asymptotic stability of the unique positive equilibrium, the boundedness and periodic nature of the solutions.

MSC:
39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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