| 一类非线性差分方程正解的渐近性 |
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| 引用本文： | 刘玉记 谈小球. 一类非线性差分方程正解的渐近性[J]. 宁波大学学报(理工版), 1999, 12(3): 20-28 |
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| 作者姓名： | 刘玉记 谈小球 |
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| 作者单位： | [1]岳阳师范学院数学系 [2]岳阳市第中学 |
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| 摘 要： | 研究了差分方程ｘｎ＋１＝ｘｎｅ＾ｒｎ（１－ａｘｎ－ｋ－ｂｘ＾２ｎ－ｋ），ｎ＝０，１，．．．，其中｛ｒｎ｝是非负实数列，ａ〉０，ｂ〉０；ｋ是非负整数，证明了：（１）设∞／∑／ｎ＝０ｒｎ＝∞，μ＝ｌｉｎ／ｎ→∞ｓｕｐｎ／∑／ｒｉ〈（３／２＋１／２（ｋ＋）／（１＋ｂＮ＾＊２），则（＊）的每一正解满足ｌｉｎｎ→∞＝ｎ＊。（２）方程ｘｎ＋１＝ｘｎ．ｅ＾４（１－ａｘｎ－ｋ－ｂｘ＾２ｎ－ｋ），ｎ＝０．１，．．．
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| 关 键 词： | 差分方程 全局渐近性 正解 非线性 充要条件 |
Asymptofic Property of Positive Solutions in a Class of Nonlinear difference Equations |
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| LIU Yu-ji,TAN Xiao-Qiu. Asymptofic Property of Positive Solutions in a Class of Nonlinear difference Equations[J]. Journal of Ningbo University(Natural Science and Engineering Edition), 1999, 12(3): 20-28 |
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| Authors: | LIU Yu-ji TAN Xiao-Qiu |
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| Affiliation: | LIU Yu-ji,TAN Xiao-Qiu2 |
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| Abstract: | The difference equation xn+1 = ) is examined, where {rn } is asequence of nonnegative numbers, a > 0, b > 0 and k is a nonnegative integer. It isproved that if ,and lim sup then everypositive solution of the difference, eqnation converges to N* as n |
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| Keywords: | difference equation globally asy mptotic properly positive solution |
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