| 一般Lyness方程的周期性与严格振动性 |
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| 引用本文： | 李先义,肖功福.一般Lyness方程的周期性与严格振动性[J].应用数学和力学,2000,21(4):409-414. |
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| 作者姓名： | 李先义 肖功福 |
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| 作者单位： | 1.华东师范大学数学系, 上海 200063; |
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| 基金项目： | 数学天元基金，中南工学院科研基金 |
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| 摘 要： | 研究了一般的Lyness方程 其中a、b∈0,∞)且a+b>0,初值x-1、x0为任意正数。得到了一些新的结果;方程(*)解的周期性的一个必要充分条件;方程(*)的所有解严格振动的充分条件。作为应用,解决了G.Ladas提出的一个公开问题。
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| 关 键 词： | 一般Lyness方程 周期性 严格振动性 公开问题 |
| 收稿时间： | 1998-05-04 |
| 修稿时间： | 1998-05-04 |
Periodicity and Strict Oscillation for Generalized Lyness Equations |
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| Li Xianyi,Xiao Gongfu.Periodicity and Strict Oscillation for Generalized Lyness Equations[J].Applied Mathematics and Mechanics,2000,21(4):409-414. |
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| Authors: | Li Xianyi Xiao Gongfu |
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| Institution: | 1.Basic Science Department, Central-South Institute of Technology, Hengyang, Hunan 421001, P R China;2.Basic Science Department, Hengyang of Hunan University, Hengyang, Hunan 421101, P R China |
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| Abstract: | A generalized Lyness equation is investigated as follows where a,b∈0,∞) with a＋b＞0 and where the initial values x-1,x0 are arbitrary positive numbers.Some new results,mainly a necessary and sufficient condition for the periodicity of the solutions of Eq.(*) and a sufficient condition for the strict oscillation of all solutions of Eq(*),are obtained.As an application,the results solve an open problem presented by G.Ladas. |
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| Keywords: | generalized Lyness equation periodicity strict oscillation open problem |
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