On the asymptotic behavior and periodic nature of a difference equation with maximum

✍ Scribed by Ali Gelişken; Cengiz Çinar; Abdullah Selçuk Kurbanli

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 376 KB
• Volume: 59
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2009.10.004

✦ Synopsis

In this paper, we investigate the asymptotic behavior and periodic nature of positive solutions of the difference equation

where A ≥ 0 and 0 ≤ α ≤ 1. We prove that every positive solution of this difference equation approaches x = 1 or is eventually periodic with a period 2, 3 or 4.