含最大值函数的递归序列解的行为(英文)

BEHAVIOR OF SOLUTIONS OF CERTAIN RECURSIONS INVOLVING THE MAXIMUM FUNCTION

本文研究下列含最大值函数的差分方程解的行为:xn+1=max(x1+an,A)xanxn-k,n=0,1,2,…,()其中a∈犤0,∞),A∈(0,∞)andk∈狖1,2,3,…狚.得到了方程()的严格振动性,环长,周期性以及方程()解的非平凡正解极限的不存在性的一些充分条件,这些结果包含和推广了一些已知的结果并部分解答了G.

the maximum function xn+1=max(x, A), n=0, 1, 2, ..., (*)where a∈[0, ∞), A∈(0, ∞) and k∈{1, 2, 3, ...}. Some cufficient conditions for the strict oscillation, the cycle length and the periodicity of Eq.(*) as well as the nonexistence of limit for nontrivial positive solutions of Eq.(*) are given, which include and extend some known ones and partly solve two open problems of G.Ladas.