摘要： A generalized Lyness equation is investigated as follows x_n+1=x_n/(a+bx_n)x_n-1, n=0,1,2,…,(*) 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.

中图分类号: 

• O175.7