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A reciprocal difference equation with maximum. (English) Zbl 1050.39015

Summary: We consider positive solutions of the following difference equation: \[ x_{n+1}=\max \left\{\frac{A}{x_n},\frac{B}{x_{n-2}} \right\};\qquad A,B>0 \] We prove that every positive solution is eventually periodic.

MSC:

39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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