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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 {\it S. Stević} [Discrete Dyn. Nat. Soc. 2007, Article ID 40963, 9 p. (2007; Zbl 1151.39011)] $x_{n+1}= A+x_{n}^{p}/x_{n-k}^{p^{k+1}}, n\in \Bbb N_{0}$, where $A,p\in (0,+\infty), k\in \Bbb N$, 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 (difference equations) 39A20 Generalized difference equations
Full Text:
##### References:
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