| 引用本文： |
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王琦,曾凡平,张更容.差分方程xn+1=(α+βxn+γxn-1)/(A+Bxn+Cxn-1)两个猜想的证明[J].广西科学,2006,13(2):90-92. [点击复制]
- WANG Qi,ZENG Fan-ping,ZHANG Geng-rong.The Confirmation of Two Conjectures about the Difference Equation xn+1= (α+βxn+γxn-1)/ (A+Bxn+Cxn-1)[J].Guangxi Sciences,2006,13(2):90-92. [点击复制]
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| 摘要: |
| 证明差分方程xn+1=(α+βxn+γxn-1)/(A+Bxn+Cxn-1),n=0,1,…当C∈(0,+∞)时每个非负解是有界的. |
| 关键词: 差分方程 周期解 正解 界性 |
| DOI： |
| 投稿时间：2005-08-02修订日期：2005-10-11 |
| 基金项目:Supported by NSFC(10361001,10226014),Guangxi Science Foundation (0249002,0007002) and Science Foundation of Guangxi University (X061022) |
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| The Confirmation of Two Conjectures about the Difference Equation xn+1= (α+βxn+γxn-1)/ (A+Bxn+Cxn-1) |
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WANG Qi1,2, ZENG Fan-ping1, ZHANG Geng-rong1
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| (1.College of Mathematics and Information Sciences, Guangxi University, Nanning, Guangxi, 530004, China;2.Department of Information and Computer Science, Guangxi University of Technology, Liuzhou, Guangxi, 545006, China) |
| Abstract: |
| Every non-negative solution of the difference equation xn+1= (α+βxn+γxn-1)/ (A+Bxn+Cxn-1), n=0, 1, … where C∈ (0, +∞), is bounded. |
| Key words: difference equation periodic solution positive solution boundedness. |
