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| 含最大值函数的递归序列解的行为 | |
| 引用本文： | 李先义,朱德明,肖功福.含最大值函数的递归序列解的行为[J].数学杂志,2003,23(2):199-206. |
| 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;南华大学数理部,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,衡阳,421101 |
| 基金项目： | SupportedbytheNNSF(grant:10071022)，MathematicalTianyuanFoundation(TY10026002-01-05-03)andShanghaiPriorityAcademicDisciplineFoundation |
| 摘 要： | 本文研究了下列含最大值函数的差分方程解的行为：xn 1=max(xn^1 1,A)/xn^axn-k,n=0,1,2,…，其中α∈0,∞]，A∈（0，∞）and k∈(1,2,3，…）。得到了方程（＊）的严格振动性，环长，周期性以及方程（＊）解的非平凡正解极限的不存在性的一些充分条件，这些结果包含和推广了一些已知的结果并部分解答了G.Ladas的两个公开问题。 |
| 关 键 词： | 递归序列 振动性 环长 周期性 非平凡正解极限的不存在性 |
BEHAVIOR OF SOLUTIONS OF CERTAIN RECURSIONS INVOLVING THE MAXIMUM FUNCTION |
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| LI Xian-Yi,ZHU De-ming,XIAO Gong-fu.BEHAVIOR OF SOLUTIONS OF CERTAIN RECURSIONS INVOLVING THE MAXIMUM FUNCTION[J].Journal of Mathematics,2003,23(2):199-206. | |
| Authors: | LI Xian-Yi ZHU De-ming XIAO Gong-fu |
| Abstract: | The behavior of solutions is investigated for the following difference equation involving the maximum function xn+1=max(x1+a n, A)/xa n xn-k, n=0, 1, 2, ..., (*)where α∈0, ∞), A∈(0, ∞) and k∈{1, 2, 3, ...}. Some cufficient conditions for the strict oscillation, the cycle length and the periodicity of Eq. (*) as well as the nonexistence of limit for nontrivial positive solutions of Eq. (*) are given, which include and extend some known ones and partly solve two open problems of G. Ladas. |
| Keywords: | recursive sequence oscillation semicycle cycle length periodicity |
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