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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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