| 引用本文： |
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伍晖,孙太祥,韩彩虹.关于差分方程xn=(A+xn-1p)/(B+xn-kp)正解的有界性[J].广西科学,2008,15(4):361-363. [点击复制]
- WU Hui,SUN Tai-xiang,HAN Cai-hong.On the Boundedness Nature of Positive Solutions of the Difference Equation xn= (A+xn-1p)/(B+xn-kp)[J].Guangxi Sciences,2008,15(4):361-363. [点击复制]
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| 摘要: |
| 证明差分方程xn=(A+xn-1p)/(B+xn-kp),n=0,1,2,…,(其中k ≥ 2,A,B,p∈(0,+∞))在pk-1 ≥ (kk)/((k-1)k-1)时,有无界的解,并且当pk-1<(kk)/((k-1)k-1)时,每个正解都有界. |
| 关键词: 差分方程 有界性 正解 |
| DOI： |
| 投稿时间：2007-12-05修订日期：2008-03-17 |
| 基金项目:Project supported by NSF of guangxi (0640205, 0728002);innovation project of guangxi graduate education(20081505930701M43) |
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| On the Boundedness Nature of Positive Solutions of the Difference Equation xn= (A+xn-1p)/(B+xn-kp) |
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WU Hui, SUN Tai-xiang, HAN Cai-hong
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| (College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| The difference equation xn= (A+xn-1p)/(B+xn-kp), n=0, 1, 2, …, are considered in this paper, where k ≥ 2 and A, B, p∈ (0, +∞). We show that if pk-1 ≥ (kk)/( (k-1)k-1), then this equation has positive unbounded solutions, and if pk-1< (kk)/( (k-1)k-1), then every positive solution of this equation is bounded. |
| Key words: difference equation boundedness positive solution |
