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Stević, Stevo; Diblík, Josef; Iričanin, Bratislav; Šmarda, Zdeněk

On the difference equation \(x_{n+1} = x_nx_{n-k}/(x_{n-k+1}(a + bx_nx_{n-k}))\). (English) Zbl 1246.39011

Abstr. Appl. Anal. 2012, Article ID 108047, 9 p. (2012).
Summary: We show that the difference equation \(x_{n+1} = x_nx_{n-k}/x_{n-k+1}(a + bx_nx_{n-k}), n \in \mathbb N_0\), where \(k \in \mathbb N\), the parameters \(a, b\) and initial values \(x_{-i}, i = \overline{0, k}\) are real numbers, can be solved in closed form considerably extending the results in the literature. By using obtained formulae, we investigate asymptotic behavior of well-defined solutions of the equation.

Cited in 18 Documents

MSC:

39A20 Multiplicative and other generalized difference equations
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\textit{S. Stević} et al., Abstr. Appl. Anal. 2012, Article ID 108047, 9 p. (2012; Zbl 1246.39011)
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References:

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