一类泛函微分方程的渐近性质

The Asymptotic Behavior of a Class of Functional Differential Equations

本文考虑形如(t)=f(x_t)的泛函微分方程,其中f是“互助”映射(依Smith)。本文的主要结果(定理3)证明了以下事实:在一定条件下,对任何正的“初始函数”φ,方程(?)(t)=f(x_t)的解x(t,φ)渐近于一个唯一的正平衡状态。

In this paper we consider functional differential equations of the form x(t)= f(x_t),where f is a cooperative map (following Smith[7]). The main result of the paper is theorem 3 which asserts that under certain conditions the solution x(t,φ) of the equation x(t)=f(x_t) asymptotically approach to a unique positive equilibrium state for any positive initial function φ.