On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1)
We consider the following nonlinear difference equation: xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} and k,t∈{1,2,…} with 0≤m<t(k+1)−1, the initial values x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞), and {pn}n=0∞ is a positive sequence of the period k+1. We give sufficient conditions under wh...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/90625 |
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| _version_ | 1832564948805353472 |
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| author | Taixiang Sun Hongjian Xi |
| author_facet | Taixiang Sun Hongjian Xi |
| author_sort | Taixiang Sun |
| collection | DOAJ |
| description | We consider the following nonlinear difference equation:
xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} and
k,t∈{1,2,…} with 0≤m<t(k+1)−1, the initial
values x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞),
and {pn}n=0∞ is a positive sequence of the period
k+1. We give sufficient conditions under which every positive
solution of this equation tends to the period k+1 solution. |
| format | Article |
| id | doaj-art-420e8db078a344e5aa321e0fd32f0abc |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-420e8db078a344e5aa321e0fd32f0abc2025-02-03T01:09:45ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/9062590625On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1)Taixiang Sun0Hongjian Xi1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, ChinaWe consider the following nonlinear difference equation: xn+1=f(pn,xn−m,xn−t(k+1)+1), n=0,1,2,…, where m∈{0,1,2,…} and k,t∈{1,2,…} with 0≤m<t(k+1)−1, the initial values x−t(k+1)+1,x−t(k+1)+2,…,x0∈(0,+∞), and {pn}n=0∞ is a positive sequence of the period k+1. We give sufficient conditions under which every positive solution of this equation tends to the period k+1 solution.http://dx.doi.org/10.1155/DDNS/2006/90625 |
| spellingShingle | Taixiang Sun Hongjian Xi On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) Discrete Dynamics in Nature and Society |
| title | On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) |
| title_full | On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) |
| title_fullStr | On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) |
| title_full_unstemmed | On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) |
| title_short | On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1) |
| title_sort | on the global behavior of the nonlinear difference equation xn 1 f pn xn m xn t k 1 1 |
| url | http://dx.doi.org/10.1155/DDNS/2006/90625 |
| work_keys_str_mv | AT taixiangsun ontheglobalbehaviorofthenonlineardifferenceequationxn1fpnxnmxntk11 AT hongjianxi ontheglobalbehaviorofthenonlineardifferenceequationxn1fpnxnmxntk11 |