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| 一类Lyness方程的一些性质 | |
| 引用本文： | 李先义,朱德明,肖功福.一类Lyness方程的一些性质[J].数学杂志,2004,24(2):147-155. |
| 作者姓名： | 李先义 朱德明 肖功福 |
| 作者单位： | 1. 华东师范大学数学系,上海,200062;南华大学数理学院,湖南,衡阳,421001 2. 华东师范大学数学系,上海,200062 3. 湖南大学衡阳分校基础部,湖南,衡阳,421001 |
| 基金项目： | SupportedbyNNSFofChina (grant:1 0 0 71 0 2 2 )，MathematicalTianyuanFoundation(grant :1 0 0 2 6 0 0 2 0 1 0 5 0 3)andShanghaiPriorityAcademicDiscipline . |
| 摘 要： | 本文主要研究下列Lyness方程的性质Xn+1=Xn\(a+b0Xn+b1Xn-1+…+bkXn-k)Xn-k-1,n=0,1,2,…,其中a,b0,b,…,bk∈0,∞),a+k∑i=0bi＞0,k∈{0,1,2,…}.文中给出了方程(*)严格振动的充分条件,以及环长和环上极值的位置.另外,还得到了方程(*)在特殊情况下分别具有4,5,6周期的必要充分条件.本文的结果改进并推广了一些已知结果. |
| 关 键 词： | 差分方程 振动性 半环 环长 极值 周期性 |
SOME PROPERTIES OF A KIND OF LYNESS EQUATION |
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| Abstract.SOME PROPERTIES OF A KIND OF LYNESS EQUATION[J].Journal of Mathematics,2004,24(2):147-155. | |
| Authors: | Abstract |
| Abstract: | In this paper, the authors mainly investigate the properties of solutions of the following Lyness equation:Xn+1=Xn\(a+b0Xn+b1Xn-1+…+bkXn-k)Xn-k-1,n=0,1,2,…,where a,b0,b,…,bk∈0,∞),a+k∑i=0bi＞0,k∈{0,1,2,…}.for the strict oscillation, the cycle length and the position of the extreme value in a semicycle of Eq. ( * ) are given. In addition, some necessary and sufficient conditions for the special cases of Eq. (*) to be periodic with prime period 4, 5 and 6, respectively, are also obtained. Some known results are improved and extended. |
| Keywords: | difference equation oscillation semicycle cycle length extreme value periodicity |
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