| 吕定洋.一类高阶有理型差分方程的全局渐近稳定性[J].南华大学学报(自然科学版),2007,21(1):106~108.[.Global Asymptotic Stability for a Kind of Rational Difference Equations with Higher Order[J].Journal of University of South China(Science and Technology),2007,21(1):106~108.] |
| 一类高阶有理型差分方程的全局渐近稳定性 |
| Global Asymptotic Stability for a Kind of Rational Difference Equations with Higher Order |
| 修订日期：2007-03-01 |
| DOI： |
| 中文关键词: 有理型差分方程,全局渐近稳定性,周期性,公开问题 |
| 英文关键词:rational difference equation,global asymptotic stability,periodicity,open problem |
| 基金项目: |
| 吕定洋 |
| 湖南师范大学数学与计算机科学学院 湖南长沙410081，湖南第一师范学院数理系，湖南长沙410205 |
| 摘要点击次数: 721 |
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| 中文摘要: |
| 本文首先获得一类三阶有理型差分方程解的全局渐近稳定性结果,解决了[M.R.S.Kulenovic and G.Ladas,Dynamics of Second Order Rational Difference E-quations,with Open Problems and Conjectures,Chapman and Hall/CRC,2002.]中的公开问题7.5.2,并证明了这类方程无周期解;然后推广这个结果到更一般的情形. |
| 英文摘要: |
| This paper first obtains global asymptotic stability for a kind of third order rational difference equation.It solves the open problem 7.5.2 given in [M.R.S.Kulenovic and G.Ladas,Dynamics of Second Order Rational Difference Equations,with Open Problems and Conjectures,Chapman and Hall/CRC,2002], and moreover proves that there do not exist periodic solutions for this kind of equation;then it extends these results to a general case. |
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