| 一类二阶非线性差分方程的全局吸引性 |
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| 引用本文： | 崔德旺,何万生,夏鸿鸣,马草川.一类二阶非线性差分方程的全局吸引性[J].纯粹数学与应用数学,2010,26(2):306-310. |
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| 作者姓名： | 崔德旺 何万生 夏鸿鸣 马草川 |
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| 作者单位： | 天水师范学院数学系,甘肃,天水,741001;天水师范学院数学系,甘肃,天水,741001;天水师范学院数学系,甘肃,天水,741001;天水师范学院数学系,甘肃,天水,741001 |
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| 基金项目： | 甘肃省自然科学研究基金，甘肃省教育厅科研项目 |
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| 摘 要： | 考虑二阶非线性差分方程xn＋1=a＋bxn/A＋xn-1,n=0,1,2,….证明了当条件a,b,A∈（0,∞）成立时方程的唯一正平衡点x^-=（b-A＋√（（b-A）2＋4a））～（1/2））/2是方程的所有正解的一个全局吸引子,所得推论证明了由Kocic和Ladas提出的一个猜想是正确的.
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| 关 键 词： | 差分方程 正平衡点 全局吸引子 |
Global attractivity in a second-order nonlinear difference equation |
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| CUI De-wang,HE Wan-sheng,XIA Hong-ming,MA Cao-chuan.Global attractivity in a second-order nonlinear difference equation[J].Pure and Applied Mathematics,2010,26(2):306-310. |
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| Authors: | CUI De-wang HE Wan-sheng XIA Hong-ming MA Cao-chuan |
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| Institution: | CUI De-wang,HE Wan-sheng,XIA Hong-ming,MA Cao-chuan(Department of Mathematics,Tianshui Normal University,Tianshui 741001,China) |
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| Abstract: | Considering second-order nonlinear difference equationX_(n+1)=a+bx_n/A+x_(n-1),n=0, 1, 2,..., this paper proves that the unique positive equilibrium X=b-A+√(b-A)~2+4a/2 is a global attractor of all positive solutions of the equation. The obtained corollary proves a conjecture which is given by Kocic and Ladas. |
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| Keywords: | difference equation positive equilibrium global attractor |
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