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Periodicity and strict oscillation for generalized lyness equations

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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, xo 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.

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Authors and Affiliations

  1. Basic Science Department, Central-South Institute of Technology, 421001, Hengyang, P R China

    Li Xianyi Associate Professor

  2. Basic Science Department, Hengyang Branch of Hunan University, 421101, Hengyan, P R China

    Xiao Gongfu

Authors
  1. Li Xianyi Associate Professor
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  2. Xiao Gongfu
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Additional information

Communicated by Zhou Huanwen

Foundation item: the Mathematical Tianyuan Foundation of China

Biography: Li Xianyi (1966-)

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Xianyi, L., Gongfu, X. Periodicity and strict oscillation for generalized lyness equations. Appl Math Mech 21, 455–460 (2000). https://doi.org/10.1007/BF02463768

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  • DOI: https://doi.org/10.1007/BF02463768

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