Global Behavior of the Difference Equation xn+1=xn-1g(xn)
We consider the following difference equation xn+1=xn-1g(xn), n=0,1,…, where initial values x-1,x0∈[0,+∞) and g:[0,+∞)→(0,1] is a strictly decreasing continuous surjective function. We show the following. (1) Every positive solution of this equation converges to a,0,a,0, …, or 0,a,0,a,… for some a∈[...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/705893 |
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| author | Hongjian Xi Taixiang Sun Bin Qin Hui Wu |
| author_facet | Hongjian Xi Taixiang Sun Bin Qin Hui Wu |
| author_sort | Hongjian Xi |
| collection | DOAJ |
| description | We consider the following difference equation xn+1=xn-1g(xn), n=0,1,…, where initial values x-1,x0∈[0,+∞) and g:[0,+∞)→(0,1] is a strictly decreasing continuous surjective function. We show the following. (1) Every positive solution of this equation converges to a,0,a,0, …, or 0,a,0,a,… for some a∈[0,+∞). (2) Assume a∈(0,+∞). Then the set of initial conditions (x-1,x0)∈(0,+∞)×(0,+∞) such that the positive solutions of this equation converge to a,0,a,0,…, or 0,a,0,a,… is a unique strictly increasing continuous function or an empty set. |
| format | Article |
| id | doaj-art-6402383da3834109a17095a09ef5df18 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6402383da3834109a17095a09ef5df182025-02-03T05:50:21ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/705893705893Global Behavior of the Difference Equation xn+1=xn-1g(xn)Hongjian Xi0Taixiang Sun1Bin Qin2Hui Wu3College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaCollege of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi 530003, ChinaCollege of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaWe consider the following difference equation xn+1=xn-1g(xn), n=0,1,…, where initial values x-1,x0∈[0,+∞) and g:[0,+∞)→(0,1] is a strictly decreasing continuous surjective function. We show the following. (1) Every positive solution of this equation converges to a,0,a,0, …, or 0,a,0,a,… for some a∈[0,+∞). (2) Assume a∈(0,+∞). Then the set of initial conditions (x-1,x0)∈(0,+∞)×(0,+∞) such that the positive solutions of this equation converge to a,0,a,0,…, or 0,a,0,a,… is a unique strictly increasing continuous function or an empty set.http://dx.doi.org/10.1155/2014/705893 |
| spellingShingle | Hongjian Xi Taixiang Sun Bin Qin Hui Wu Global Behavior of the Difference Equation xn+1=xn-1g(xn) Abstract and Applied Analysis |
| title | Global Behavior of the Difference Equation xn+1=xn-1g(xn) |
| title_full | Global Behavior of the Difference Equation xn+1=xn-1g(xn) |
| title_fullStr | Global Behavior of the Difference Equation xn+1=xn-1g(xn) |
| title_full_unstemmed | Global Behavior of the Difference Equation xn+1=xn-1g(xn) |
| title_short | Global Behavior of the Difference Equation xn+1=xn-1g(xn) |
| title_sort | global behavior of the difference equation xn 1 xn 1g xn |
| url | http://dx.doi.org/10.1155/2014/705893 |
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