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Global attractivity of a rational difference equation with higher order and its application to several conjectures

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摘要 We study the global dynamics of a rational diference equation with higher order,which includes many rational diference equations as its special cases.By some complicate computations and mathematical skills,we show that its unique nonnegative fixed point is globally attractive.As application,our results not only improve many known ones,but also solve several“Open Problems and Conjectures”given by Professors Ladas and Camouzis,et al.
作者 LI Xian-yi LI Dan-yang
机构地区 Department of Big Data Science
出处 《Applied Mathematics(A Journal of Chinese Universities)》 2025年第4期886-900,共15页 高校应用数学学报(英文版)(B辑)
基金 Supported by the National Natural Science Foundation of China(61473340) Distinguished Professor Foundation of Qianjiang Scholar in Zhejiang Province(F703108L02)。
关键词 rational difference equation with higher order global attractivity globally asymptoticaly stable Schwarzian derivative CONJECTURE
分类号 O175.7 [理学—基础数学]
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  • 1LADAS G. Open Problems and Conjectures, Proceedings of the First International Conference on Difference Equations and Applications [M]. Gordon and Breach Publishers, Inc., 1994.
  • 2LADAS G. Open Problems and Conjectures[J]. J. Difference Equa. Appl., 1995, 3: 317-321.
  • 3KOCIC V L, LADAS G. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications [M]. Kluwer Academic Publishers group, Dordrecht, 1993.
  • 4KOCIC V L, LADAS G. Global Attractivlty in Nonlinear Delay Difference Equations [J]. Proc. Amer. Math. Soc., 1992, 115: 1083-1088.
  • 5KOCIC V L, LADAS G, RODRIGUES I W. On rational recursive sequences [J]. J. Math. Anal. Appl., 1993, 173: 127-157.
  • 6Ladas,G.,Open problems andconjectures,J.Differ.Equations Appl.,1998,4(1):95-97.
  • 7Kocic, V.L.,Ladas,G.,Global Behavior of Nonlinear Difference Equations of HigherOrder with Applications,Kluwer Academic Publishers,Dordrecht,1993.
  • 8Li Xianyi, Tang Hengsheng, Liu Yachun, et al., A Conjecture byG.Ladas,Appl.Math.J.Chinese Univ.Ser B.,1998,13:39-44.
  • 9Kocic, V.L.,Ladas, G.,Global Behavior of NonlinearDifference Equations of Higher Order with Applications, Kluwer AcademicPublishers,Dordrecht,1993.
  • 10Ladas,G.,Open problem and conjectures,Proceedings of the Ist InternationalConference on Difference Equations and Applications,San Antonio Texas,May 25～28,1994,Gordonand Breach Publishers,Inc,1994.

共引文献12

Applied Mathematics(A Journal of Chinese Universities)
2025年 第4期

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