The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1)
In this paper, we consider the nonlinear difference equation xn+1=f(xn−l+1,xn−2k+1), n=0,1,…, where k,l∈{1,2,…} with 2k≠l and gcd(2k,l)=1 and the initial values x−α,x−α+1,…,x0∈(0,+∞) with α=max{l−1,2k−1}. We give sufficient...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2008-03-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2008/143723 |
| _version_ | 1818188136631500800 |
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| author | Taixiang Sun Hongjian Xi |
| author_facet | Taixiang Sun Hongjian Xi |
| author_sort | Taixiang Sun |
| collection | DOAJ |
| description | In this paper, we consider the nonlinear difference equation xn+1=f(xn−l+1,xn−2k+1), n=0,1,…, where k,l∈{1,2,…} with 2k≠l and gcd(2k,l)=1 and the initial values x−α,x−α+1,…,x0∈(0,+∞) with α=max{l−1,2k−1}. 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. |
| first_indexed | 2024-12-11T23:22:08Z |
| format | Article |
| id | doaj.art-29dad5907c0c49e78ac5209eb618e134 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 |
| language | English |
| last_indexed | 2024-12-11T23:22:08Z |
| publishDate | 2008-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-29dad5907c0c49e78ac5209eb618e1342022-12-22T00:46:19ZengSpringerOpenAdvances in Difference Equations1687-18392008-03-01200810.1155/2008/143723The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1)Taixiang SunHongjian XiIn this paper, we consider the nonlinear difference equation xn+1=f(xn−l+1,xn−2k+1), n=0,1,…, where k,l∈{1,2,…} with 2k≠l and gcd(2k,l)=1 and the initial values x−α,x−α+1,…,x0∈(0,+∞) with α=max{l−1,2k−1}. 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.http://dx.doi.org/10.1155/2008/143723 |
| spellingShingle | Taixiang Sun Hongjian Xi The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1) Advances in Difference Equations |
| title | The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1) |
| title_full | The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1) |
| title_fullStr | The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1) |
| title_full_unstemmed | The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1) |
| title_short | The Periodic Character of the Difference Equation xn+1=f(xn−l+1,xn−2k+1) |
| title_sort | periodic character of the difference equation xn 1 f xna¢a a l 1 xna¢a a 2k 1 |
| url | http://dx.doi.org/10.1155/2008/143723 |
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