The Periodic Character of the Difference Equation <inline-formula> <graphic file="1687-1847-2008-143723-i1.gif"/></inline-formula>

• Main Authors: Xi Hongjian, Sun Taixiang
• Format: Article
• Language: English
• Published: SpringerOpen 2008-01-01
• Series: Advances in Difference Equations
• Online Access: http://www.advancesindifferenceequations.com/content/2008/143723

<p>Abstract</p> <p>In this paper, we consider the nonlinear difference equation <inline-formula> <graphic file="1687-1847-2008-143723-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1847-2008-143723-i3.gif"/></inline-formula> where <inline-formula> <graphic file="1687-1847-2008-143723-i4.gif"/></inline-formula> with <inline-formula> <graphic file="1687-1847-2008-143723-i5.gif"/></inline-formula> and <inline-formula> <graphic file="1687-1847-2008-143723-i6.gif"/></inline-formula> and the initial values <inline-formula> <graphic file="1687-1847-2008-143723-i7.gif"/></inline-formula> with <inline-formula> <graphic file="1687-1847-2008-143723-i8.gif"/></inline-formula>. We give sufficient conditions under which every positive solution of this equation converges to a ( not necessarily prime ) 2-periodic solution, which extends and includes corresponding results obtained in the recent literature.</p>