Existence of Monotone Solutions of a Difference Equation
We consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/917560 |
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| _version_ | 1849695994838515712 |
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| author | Taixiang Sun Hongjian Xi Weizhen Quan |
| author_facet | Taixiang Sun Hongjian Xi Weizhen Quan |
| author_sort | Taixiang Sun |
| collection | DOAJ |
| description | We consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this way some results of the literature. |
| format | Article |
| id | doaj-art-cd9daad380f64eeeb33ee2815f4ab81d |
| institution | DOAJ |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-cd9daad380f64eeeb33ee2815f4ab81d2025-08-20T03:19:35ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2008-01-01200810.1155/2008/917560917560Existence of Monotone Solutions of a Difference EquationTaixiang Sun0Hongjian Xi1Weizhen Quan2Department of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaDepartment of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, ChinaWe consider the nonlinear difference equation xn+1=f(xn−k,xn−k+1,…,xn), n=0,1,…, where k∈{1,2,…} and the initial values x−k,x−k+1,…,x0∈(0,+∞). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this way some results of the literature.http://dx.doi.org/10.1155/2008/917560 |
| spellingShingle | Taixiang Sun Hongjian Xi Weizhen Quan Existence of Monotone Solutions of a Difference Equation Discrete Dynamics in Nature and Society |
| title | Existence of Monotone Solutions of a Difference Equation |
| title_full | Existence of Monotone Solutions of a Difference Equation |
| title_fullStr | Existence of Monotone Solutions of a Difference Equation |
| title_full_unstemmed | Existence of Monotone Solutions of a Difference Equation |
| title_short | Existence of Monotone Solutions of a Difference Equation |
| title_sort | existence of monotone solutions of a difference equation |
| url | http://dx.doi.org/10.1155/2008/917560 |
| work_keys_str_mv | AT taixiangsun existenceofmonotonesolutionsofadifferenceequation AT hongjianxi existenceofmonotonesolutionsofadifferenceequation AT weizhenquan existenceofmonotonesolutionsofadifferenceequation |