Acta mathematica scientia,Series B ›› 2005, Vol. 25 ›› Issue (1): 59-66.

• Articles • Previous Articles     Next Articles

GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION

 LI Mo-Tong, ZHANG Yan-Gong, SU Wei-Hui   

  • Online:2005-01-20 Published:2005-01-20
  • Supported by:

    Supported by the NNSF of China (10171040), the NSF of Gansu Province of China
    (ZS011-A25-007-Z), the Foundation for University Key Teacher by Ministry of Education of China, and the
    Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of
    Ministry of Education of China.

Abstract:

In this paper the global attractivity of the nonlinear difference equation

x_{n+1}=\frac{a+bx_n}{A+x_{n-k}},\quad n=0,1,\cdots ,

is investigated, where $a,b,A\in (0,\infty ),$ $k$ is an positive integer

and the initial conditions $x_{-k},\cdots,x_{-1}$ and $x_0$ are arbitrary

positive numbers. It is shown that the unique positive equilibrium of the

equation is global attractive. As a corollary, the result gives a positive

confirmation on the conjecture presented by Kocic and Ladas [1,p154].

Key words: Difference equation;global attractivity;stability;equilibrium.

CLC Number: 

  • 39A10
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