## Abstract and Applied Analysis

### Global Behavior of the Max-Type Difference Equation ${x}_{n+1}=\max \{1/{x}_{n},{A}_{n}/{x}_{n-1}\}$

#### Abstract

We study global behavior of the following max-type difference equation ${x}_{n+1}=\max \{1/{x}_{n},{A}_{n}/{x}_{n-1}\}$, $n=0,1,\ldots ,$ where ${\{{A}_{n}\}}_{n=0}^{\infty }$ is a sequence of positive real numbers with $0\leq \inf {A}_{n}\leq \sup {A}_{n}\lt1$. The special case when ${\{{A}_{n}\}}_{n=0}^{\infty}$ is a periodic sequence with period $k$ and ${A}_{n}\in (0,1)$ for every $n\geq 0$ has been completely investigated by Y. Chen. Here we extend his results to the general case.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 152964, 10 pages.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1268745553

Digital Object Identifier
doi:10.1155/2009/152964

Mathematical Reviews number (MathSciNet)
MR2506993

Zentralblatt MATH identifier
1167.39303

#### Citation

Sun, Taixiang; Qin, Bin; Xi, Hongjian; Han, Caihong. Global Behavior of the Max-Type Difference Equation ${x}_{n+1}=\max \{1/{x}_{n},{A}_{n}/{x}_{n-1}\}$. Abstr. Appl. Anal. 2009 (2009), Article ID 152964, 10 pages. doi:10.1155/2009/152964. https://projecteuclid.org/euclid.aaa/1268745553

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