Global asymptotic stability of nonlinear neutral differential equation

摘要

In this paper, the following nonlinear neutral differential equation x'(t) = -a(t)x(t) + c(t)x'(t - t_1(t)) + q(t,x(t), x(t - t_2(t))) is considered. By using fixed point theory, we give some new conditions to ensure that the zero solution is globally asymptotically stable in C~1. By weakening the assumptions on the neutral coefficient c and the delay τ_1 and by obtaining more manageable criteria, some existing results are improved and generalized.