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More on the difference equation \(y_{n+1}=(p+y_{n-1})/(qy_n+y_{n-1})\). (English) Zbl 1022.39005

The authors study the nonlinear rational difference equation \(x_{n+1}=(\alpha + \gamma x_{n-1})/(B x_n +C x_{n-1})\). First, after a suitable change of variables, they transform such equation into the equivalent one \( y_{n+1}=(p + y_{n-1})/(q y_n + y_{n-1})\).
Under this new formulation they obtain some existence and stability results for a period two solution.

MSC:

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