一类具平均增长率的离散时带Logistic方程的振动性

Oscillation in the Logistic Delay Difference Equation with Average Growth

本文研究离散时带Logistic方程 y_(n+1)=y_ne^(r(1-y_(n-k))).这里r,k>0为常数,我们证明了方程(1)的每一个正解关于其平衡常数1振动的充要条件为r>k^k/(k+1)^(k+1)

Consider the Logistic delay difference equation with average growth yn+1 = yner(1-yn-k) where r∈ (0,+∞),k∈{1,2,…} ,We prove that every positive solution of (1) Oscillates about its equilibrium1 if and only if