## On the recursive sequence $$x_{n+1}=\alpha+\frac{x^p_{n-1}}{x_n^p}$$.(English)Zbl 1078.39013

The asymptotic behaviour of the solutions of the difference equation in the title is investigated for positive $$p$$ and nonnegative $$\alpha$$. Moreover, a convergence theorem is proved concerning the equation $$x_{n+1}=\alpha+f(x_{n-k}/x_n)$$.

### MSC:

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

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