Li Xianyi, Xiao Gongfu. Periodicity and Strict Oscillation for Generalized Lyness Equations[J]. Applied Mathematics and Mechanics, 2000, 21(4): 409-414.
 Citation: Li Xianyi, Xiao Gongfu. Periodicity and Strict Oscillation for Generalized Lyness Equations[J]. Applied Mathematics and Mechanics, 2000, 21(4): 409-414.

# Periodicity and Strict Oscillation for Generalized Lyness Equations

• Rev Recd Date: 1999-12-01
• Publish Date: 2000-04-15
• A generalized Lyness equation is investigated as follows 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.
•  [1] Ladas G.Open problems and conjectures[A].In:Proceedings of the First International Conference on Difference Equations[C].Basel:Gordon and Breach Science Publishers,1994,337～349. [2] Grove E A,Janowski E J,Kent C M,et al.On the rational recursive sequence xn＋1＝(αxn＋β)/[(γxn＋δ)xn-1] [J].Comm Appl Nonlinear Anal,1994,1(1):61～72. [3] 李先义,肖功福,唐衡生,等.关于Ladas G的一个公开问题[J].中南工学院学报,1997,11(1):26～31. [4] Ladas G.Open problems and conjectures[J].J Diff Equ Appl,1995,1(1):1～3. [5] Li Xianyi,Tang Hengsheng,Liu Yachun,et al.A conjecture by G Ladas[J].Applied Mathematics a Journal of Chinese University,Ser B,1998,13(1):39～44. [6] Kocic V L,Ladas G.Global Behavior of Nonlinear Difference Equations of Highe Order[M].Dordrecht:Kluwer Academic Publishers,1993.

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