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| 一类高阶有理差分方程解的收敛性(英文) | |
| 引用本文： | 王琦,张更容,曾凡平,陈占和.一类高阶有理差分方程解的收敛性(英文)[J].应用数学,2012,25(3):488-495. |
| 作者姓名： | 王琦 张更容 曾凡平 陈占和 |
| 作者单位： | 1. 广西工学院理学院,广西柳州,545006 2. 广西大学数学与信息科学学院,广西南宁,530004 3. 柳州师范高等专科学校数学系,广西柳州,545005 |
| 基金项目： | Supported by the Natural Science Foundation of China(11161029);the Natural Science Foundation of Guangxi(2010GXNSFA013109,2010GXNSFA013106);the Natural Science Foundation of Guangxi University of Technology(1166218) |
| 摘 要： | 本文考查下列高阶有理差分方程xn+1=(α+B1xn-1+B3xn-3+…+B2k+1xn-2k-1)/(A+B0xn+B2xn-2+…+B2kxn-2k,),n=0,1,…,其中k是非负整数,参数α,A,Bi,i=0,1,2,…,2k+1和初始值x-2k-1,x-2k,x-2k+1,…,x0是非负实数.给出充分条件,在此条件下当且仅当∑k+1i=1B2i-1=A时,方程的每个解收敛于方程的一个二周期解. |
| 关 键 词： | 差分方程 收敛性 二周期解 有界性 |
Convergence of the Solutions of a Higher-order Rational Difference Equation |
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| WANG Qi , ZHANG Gengrong , ZENG Fanping , CHEN Zhanhe.Convergence of the Solutions of a Higher-order Rational Difference Equation[J].Mathematica Applicata,2012,25(3):488-495. | |
| Authors: | WANG Qi ZHANG Gengrong ZENG Fanping CHEN Zhanhe |
| Institution: | 1.College of Science,Guangxi University of Technology,Liuzhou 545006,China;2.Institute of Mathematics,Guangxi University,Nanning 530004,China;3.Department of Mathematics,Liuzhou Teachers of College,Liuzhou 545004,China) |
| Abstract: | This paper is concerned with the following higher-order rational difference equation:xn+1=(α+B1xn-1+B3xn-3+…+B2k+1xn-2k-1)/(A+B0xn+B2xn-2+…+B2kxn-2k,),n=0,1,…,where k is a non-negative integer,the parameters α,A,Bi,i=0,1,2,…,2k+1 and the initial conditions x-2k-1,x-2k,x-2k+1,…,x0 are non-negative real numbers.We give the sufficient condition under which every non-negative solution of the equation converges to a period-two solution of the equation if and only if ∑k+1i=1B2i-1=A. |
| Keywords: | Difference equation Convergence Period-two solution Boundedness |
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