Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)

Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)

We study the following difference equation xn+1=(p+xn-1)/(qxn+xn-1), n=0,1,…, where p,q∈(0,+∞) and the initial conditions x-1,x0∈(0,+∞). We show that every positive solution of the above equation either converges to a finite limit or to a two cycle, which confirms that the Conjecture 6.10.4 proposed...

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Main Authors: Taixiang Sun, Hongjian Xi, Hui Wu, Caihong Han
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2010/237129
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spelling doaj-71aa6fde2aec47899156a58fceba34052020-11-25T01:00:59ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/237129237129Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)Taixiang Sun0Hongjian Xi1Hui Wu2Caihong Han3College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, Guangxi College of Finance and Economics, Nanning 530003, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaWe study the following difference equation xn+1=(p+xn-1)/(qxn+xn-1), n=0,1,…, where p,q∈(0,+∞) and the initial conditions x-1,x0∈(0,+∞). We show that every positive solution of the above equation either converges to a finite limit or to a two cycle, which confirms that the Conjecture 6.10.4 proposed by Kulenović and Ladas (2002) is true.http://dx.doi.org/10.1155/2010/237129
collection DOAJ
language English
format Article
sources DOAJ
author Taixiang Sun
Hongjian Xi
Hui Wu
Caihong Han
spellingShingle Taixiang Sun
Hongjian Xi
Hui Wu
Caihong Han
Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)
Abstract and Applied Analysis
author_facet Taixiang Sun
Hongjian Xi
Hui Wu
Caihong Han
author_sort Taixiang Sun
title Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)
title_short Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)
title_full Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)
title_fullStr Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)
title_full_unstemmed Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)
title_sort global behavior of the difference equation xn+1=(p+xn-1)/(qxn+xn-1)
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2010-01-01
description We study the following difference equation xn+1=(p+xn-1)/(qxn+xn-1), n=0,1,…, where p,q∈(0,+∞) and the initial conditions x-1,x0∈(0,+∞). We show that every positive solution of the above equation either converges to a finite limit or to a two cycle, which confirms that the Conjecture 6.10.4 proposed by Kulenović and Ladas (2002) is true.
url http://dx.doi.org/10.1155/2010/237129
work_keys_str_mv AT taixiangsun globalbehaviorofthedifferenceequationxn1pxn1qxnxn1
AT hongjianxi globalbehaviorofthedifferenceequationxn1pxn1qxnxn1
AT huiwu globalbehaviorofthedifferenceequationxn1pxn1qxnxn1
AT caihonghan globalbehaviorofthedifferenceequationxn1pxn1qxnxn1
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