一类非自治非线性时滞微分方程的全局吸引性

GLOBAL ATTRACTIVITY IN A NONAUTONOMOUS NONLINEAR DELAY DIFFERENTIAL EQUATION

本文研究了非自治非线性时滞微分方程 x＇（t）=r（t）（1+x（t））f（xt）,t≥0,得到其零解全局吸引的一个充分条件,推广了[1]的方法.把结果应用于几类广义时滞Lo-gistic方程,或得到了一些新的结果,或改进了一些已知结果.

Abstract In this paper, a nonautonomous nonlinear delay differential equationx'(t) = r(t)(l + x(t))f(xt), t≥0is considered and a sufficient condition for all positive solution of above the equation tend to zero as t→∞ is obtained.