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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
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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. 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.
作者 吕定洋
机构地区 湖南师范大学数学与计算机科学学院
出处 《南华大学学报（自然科学版）》 2007年第1期106-108,共3页 Journal of University of South China：Science and Technology
关键词 有理型差分方程 全局渐近稳定性 周期性 公开问题 rational difference equation global asymptotic stability periodicity open problem
分类号 O175.7 [理学—基础数学]
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  • 1Ladas,G.,Open problems andconjectures,J.Differ.Equations Appl.,1998,4(1):95-97.
  • 2Kocic, V.L.,Ladas,G.,Global Behavior of Nonlinear Difference Equations of HigherOrder with Applications,Kluwer Academic Publishers,Dordrecht,1993.
  • 3Li Xianyi, Tang Hengsheng, Liu Yachun, et al., A Conjecture byG.Ladas,Appl.Math.J.Chinese Univ.Ser B.,1998,13:39-44.
  • 4De Vault R, Ladas G, Schultz S W. On the recursive sequence xn+1＝(A/xpn)+B/(xqn-1)[A].In: Proceedings of the Second International Conference on Difference Equations[C]. Basel: Gorden and Breach Science Publishers,1996.
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  • 6Ladas G. Open problems and conjectures[A]. In: Proceedings of the First International Conference on Difference Equations[C]. Basel: Gorden and Breach Science Publishers,1995,337-349.
  • 7Arciero M, Ladas G, Schultz S W. Some open problems about the solutions of the delay difference equation xn+1＝A/(x2n)+1/(xpn-k)[J]. Proceedings of the Georgian Academy of Science Mathematics, 1993,1:257-262.
  • 8Brand L. A sequence defined by a difference equation[J]. Amer Math Monthly,1995,62:489-492.
  • 9De Vault R, Kocic V L, Ladas G. Global stability of a recursive sequence[J]. Dynamics Systems and Applications,1992,1:13-21.
  • 10Ladas G. Open problems and conjectures[A]. In: Proceedings of the First International Conference on Differnce Equations[C].Basel:Gorden and Breach Science Publishers,1995,337-349.

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南华大学学报（自然科学版）
2007年 第1期

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