一般Lyness方程的周期性与严格振动性

基金项目: 数学天元基金;中南工学院科研基金

Periodicity and Strict Oscillation for Generalized Lyness Equations

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

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。
- 一般Lyness方程 /
- 周期性 /
- 严格振动性 /
- 公开问题
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.
- generalized Lyness equation /
- periodicity /
- strict oscillation /
- open problem

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