Periodicity and Strict Oscillation for Generalized Lyness Equations

Li Xianyi; Xiao Gongfu

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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.

Citation:

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

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Periodicity and Strict Oscillation for Generalized Lyness Equations

Li Xianyi^1,2,
Xiao Gongfu³

1.
Basic Science Department, Central-South Institute of Technology, Hengyang, Hunan 421001, P R China;
2.
Basic Science Department, Hengyang of Hunan University, Hengyang, Hunan 421101, P R China

Received Date: 1998-05-04
Rev Recd Date: 1999-12-01
Publish Date: 2000-04-15

Abstract

Abstract

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.
- generalized Lyness equation,
- periodicity,
- strict oscillation,
- open problem

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References(6)

References

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