Abstract and Applied Analysis

On the Difference Equation x n + 1 = x n x n - k / ( x n - k + 1 a + b x n x n - k )

Stevo Stević, Josef Diblík, Bratislav Iričanin, and Zdenĕk Šmarda

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Abstract

We show that the difference equation x n + 1 = x n x n - k / x n - k + 1 ( a + b x n x n - k ) , n 0 , where k , the parameters a , b and initial values x - i , i = 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.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 108047, 9 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495815

Digital Object Identifier
doi:10.1155/2012/108047

Zentralblatt MATH identifier
1246.39011

Citation

Stević, Stevo; Diblík, Josef; Iričanin, Bratislav; Šmarda, Zdenĕk. On the Difference Equation ${x}_{n+1}={x}_{n}{x}_{n-k}/({x}_{n-k+1}(a+b{x}_{n}{x}_{n-k}))$. Abstr. Appl. Anal. 2012 (2012), Article ID 108047, 9 pages. doi:10.1155/2012/108047. https://projecteuclid.org/euclid.aaa/1355495815


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