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On the recursive sequence $$x_{n+1}=B+\frac{x_{n-k}}{\alpha_0x_n+\cdots+\alpha_{k-1}x_{n-k+1}+\gamma}$$. (English) Zbl 1068.39012
There are conditions such that for the difference equation in the title every positive solution converges to the equilibrium $$K$$ resp. to a $$(k+1)$$-periodic solution with $$k$$ consecutive zeros, that every nonoscillatory solution converges to $$K$$, resp. that there exists a solution with divergent $$x_{2n}$$ and $$x_{2n+1}\to B$$ as $$n\to\infty$$.

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39A20 Multiplicative and other generalized difference equations, e.g., of Lyness type
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##### References:
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