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The recursive sequence \(x_{n+1} = g(x_{n},x_{n-1})/(A + x_{n})\). (English) Zbl 1029.39007
The author considers the second order nonlinear difference equation \[ x_{n+1}=\frac{g(x_n,x_{n-1})}{A+x_n},\qquad n=0,1,\dots, \] where \(A>0\) and \(g\: {\mathbb R}^2_+\to{\mathbb R}_+\) is a continuous function. The main result of the paper provides sufficient conditions on \(g\) under which every positive solution tends to a period two solution.

MSC:
39A11 Stability of difference equations (MSC2000)
39B05 General theory of functional equations and inequalities
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