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Quantitative bounds for positive solutions of a Stević difference equation. (English) Zbl 1194.39010

Summary: This paper studies the behavior of positive solutions to the following particular case of a difference equation by S. Stević [Discrete Dyn. Nat. Soc. 2007, Article ID 40963, 9 p. (2007; Zbl 1151.39011)] \(x_{n+1}= A+x_{n}^{p}/x_{n-k}^{p^{k+1}}, n\in \mathbb N_{0}\), where \(A,p\in (0,+\infty), k\in \mathbb N\), and presents theoretically computable explicit lower and upper bounds for the positive solutions to this equation. Besides, a concrete example is given to show the computing approaches which are effective for small parameters. Some analogous results are also established for the corresponding Stević max-type difference equation.

MSC:

39A22 Growth, boundedness, comparison of solutions to difference equations
39A20 Multiplicative and other generalized difference equations

Citations:

Zbl 1151.39011
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References:

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