## 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

### Keywords:

Periodic solution; Equilibrium solution
Full Text:

### References:

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