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| 一类高阶非线性差分方程的振动性 | |
| 引用本文： | 李先义,朱德明,肖功福.一类高阶非线性差分方程的振动性[J].楚雄师范学院学报,2001,16(3):1-7. |
| 作者姓名： | 李先义 朱德明 肖功福 |
| 作者单位： | 1. 华东师范大学教学系,上海,200062;南华大学数理部,湖南,衡阳,421001 2. 华东师范大学教学系,上海,200062 3. 湖南大学衡阳分校基础部,湖南,衡阳,421101 |
| 基金项目： | ThisworkissupportedbyNNSF (grant:1 0 0 71 0 2 2 )andMathematicalTianyuanFoundationofChina. |
| 摘 要： | 本文主要研究下列高阶非线性差分方程解的性质:Xn+1=Xn/f(X,Xn-1,…，Xn-k)Xn-k-1,n=0,1,2,…,(*)其中函数f某些假设,k∈{0,1,2,…}.得到了方程(*)严格振动的充分条件,环长以及环上极值位置.一些已知的结果被改进和推广. |
| 关 键 词： | 非线性差分方程 高价 振动性 半环 环长 极值 |
Oscillation for a Class of Nonlinear Delay Difference Equation with Higher Order |
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| Abstract.Oscillation for a Class of Nonlinear Delay Difference Equation with Higher Order[J].journal of chuxiong normal university,2001,16(3):1-7. | |
| Authors: | Abstract |
| Abstract: | In this paper the authors mainly investigate the properties of solutions of the following nonlinear delay difference equation with higher order:Xn+1=Xn/f(X,Xn-1,…，Xn-k)Xn-k-1,n=0,1,2,…,where f satisfies certain hypoheses for k∈{0,1,2,…}.Some sufficient conditions for the strict oscillation, the cycle length and the position of the extreme in a semicycle of the equation are obtained. Some known results are improved and extended. |
| Keywords: | nonlinear difference equation higher order oscillation semicycle cycle length extreme value |
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