| GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION |
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| 引用本文： | 李万同 张艳红 苏有慧. GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION[J]. 数学物理学报(B辑英文版), 2005, 25(1): 59-66. DOI: 10.1016/S0252-9602(17)30261-8 |
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| 作者姓名： | 李万同 张艳红 苏有慧 |
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| 作者单位： | [1]DepartmentofMathematics,LanzhouUniversity,Lanzhou730000,China [2]DepartmentofMathematics,LanzhouUniversity,Lanzhou730000,China／／DepartmentofMathematics,HexiUniversity,Zhangye734000,China |
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| 基金项目： | 国家自然科学基金，甘肃省自然科学基金，教育部大学教师基金，高等学校优秀青年教师教学科研奖励计划 |
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| 摘 要： | In this paper the global attractivity of the nonlinear difference equation xn 1 = a bxn / A xn-k, n =0, 1, …，is investigated, where a, b, A ∈ (0, ∞), k is an positive integer and the initial conditions x- k, …，x- 1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].
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| 关 键 词： | 全局吸引性 非线性差分方程 稳定性 平衡性 有理递归序列 |
| 收稿时间： | 2002-07-10 |
GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION |
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| Li Wantong,Zhang Yanhong,Su Youhui. GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION[J]. Acta Mathematica Scientia, 2005, 25(1): 59-66. DOI: 10.1016/S0252-9602(17)30261-8 |
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| Authors: | Li Wantong Zhang Yanhong Su Youhui |
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| Affiliation: | 2. Department of Mathematics, Lanzhou University, Lanzhou 730000, China;3. Department of Mathematics, Hexi University, Zhangye 734000, China;1. State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China;2. State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China;3. Department of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China |
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| Abstract: | In this paper the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0, ∞), k is an positive integer and the initial conditions equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154]. |
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| Keywords: | Difference equation global attractivity stability equilibrium |
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