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On the recursive sequence $x_n=A+x_{n-k}^p/x_{n-1}^r$. (English) Zbl 1294.39006
Summary: This paper studies the dynamic behavior of the positive solutions to the difference equation $x_n=A+x_{n-k}^p/x_{n-1}^r$, $n=1,2,\ldots,$ where $A,p$ and $r$ are positive real numbers, and the initial conditions are arbitrary positive numbers. We establish some results regarding the stability and oscillation character of this equation for $p\in [0,1)$.
MSC:
39A21Oscillation theory (difference equations)
39A30Stability theory (difference equations)
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Full Text: DOI
References:
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