| 关于差分方程χn=A+χpn-1/B+χpn-k正解的有界性 |
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| 引用本文： | 伍晖,孙太祥,韩彩虹.关于差分方程χn=A+χpn-1/B+χpn-k正解的有界性[J].广西科学,2008,15(4). |
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| 作者姓名： | 伍晖 孙太祥 韩彩虹 |
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| 基金项目： | 广西自然科学基金
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innovation project of guangxi graduate education
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| 摘 要： | 证明差分方程 χn=A+χpn-1/B+χpn-k,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.
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| 关 键 词： | 差分方程 有界性 正解 |
On the Boundedness Nature of Positive Solutions of the Difference Equation χn=A+χpn-1/B+χpn-k |
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| WU Hui,SUN Tai-xiang,HAN Cai-hong.On the Boundedness Nature of Positive Solutions of the Difference Equation χn=A+χpn-1/B+χpn-k[J].Guangxi Sciences,2008,15(4). |
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| Authors: | WU Hui SUN Tai-xiang HAN Cai-hong |
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| Abstract: | The difference equation χn=A+χpn-1/B+χpn-k,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. |
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| Keywords: | difference equation boundedness positive solution |
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