一般Lyness方程的周期性与振动性

Periodicity and Oscillation for a Generalized Lyness Equation

本文研究一般的 Ｌｙｎｅｓｓ方程 其中ａ，β，ｒ，δ ∈［０，∝）且α＋β＞０，γ＋δ＞０．获得了方程（*）解具周期性的充要条件和具严格振动性的充分条件，作为应用，我们得到了 Ｇ． Ｌａｄａｓ在［４］中提出的一个悬而未决问题的一些解．

in this paper a generalized Lyness equation of tile form whereα, β, r, δ ∈ [0, ∝) withα + β > 0 andγ + δ > 0, is investigated. A necessary and sufficient condition for the periodicity of solutions and a sufficient condition for the strict oscillation of all solutions to Eq. (*) are obtained. As an application of our results,some solutions to an open problem given by G.Ladas in [4] are given.