Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (4): 455-460.

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PERIODICITY AND STRICT OSCILLATION FOR GENERALIZED LYNESS EQUATIONS

Li Xianyi1, Xiao Gongfu 2   

  1. 1. Basic Science Department, Central-South Institute of Technology, Hengyang 421001, P. R. China;
    2. Basic Science Department, Hengyang Branch of Hunan University, Hengyang 421101, P. R. China
  • Received:1998-05-04 Revised:1999-12-01 Online:2000-04-18 Published:2000-04-18
  • Supported by:
    the Mathematical Tianyuan Foundation of China

Abstract: A generalized Lyness equation is investigated as follows xn+1=xn/(a+bxn)xn-1, n=0,1,2,…,(*) where a,b∈[0,∞) with a+b>0 and where the initial values x-1,x0 are arbitrary positive numbers. Some new results, mainly a necessary and sufficient condition for the periodicity of the solutions of Eq.(*) and a sufficient condition for the strict oscillation of all solutions of Eq(*),are obtained. As an application, the results solve an open problem presented by G.Ladas.

2010 MSC Number: 

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