On the periodic cycle of \(x_{n+1}=(a_{n}+b_{n} x_{n})/c_{n} x_{n-1}\). (Q1428172)
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scientific article; zbMATH DE number 2056323
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the periodic cycle of \(x_{n+1}=(a_{n}+b_{n} x_{n})/c_{n} x_{n-1}\). |
scientific article; zbMATH DE number 2056323 |
Statements
On the periodic cycle of \(x_{n+1}=(a_{n}+b_{n} x_{n})/c_{n} x_{n-1}\). (English)
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14 March 2004
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The author studies the behaviour of solutions of the second order difference equation \(x_{n+1}=(a_n+b_nx_n)/(c_nx_{n-1}),\) \(n=0,1,2,\dots\), where the sequences \(a_n, b_n\) and \(c_n\) are periodic. The proof of the main result Theorem 2.1 is not correct because he uses Lemma 2.1 in an incorrect manner.
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periodic cycle
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second order difference equation
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