Periodicity and strict oscillation for generalized lyness equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Periodicity and strict oscillation for generalized lyness equations

Authors:

Li Xianyi Associate Professor Xiao Gongfu

Affiliation:

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

Abstract:

A generalized Lyness equation is investigated as follows

$x_{n + 1} = frac{{x_n }}{{(a + bx_n )x_{n - 1} }}, n = 0,1,2, cdot cdot cdot$

((*))

where a, b ∈[0,∞) with a+b>0 and where the initial values x₋₁, x_o 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. Foundation item: the Mathematical Tianyuan Foundation of China Biography: Li Xianyi (1966-)

Keywords:

generalized Lyness equation periodicity strict oscillation open problem

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