Global asymptotic stability of nonlinear neutral differential equation

In this paper, the following nonlinear neutral differential equationx′(t)=-a(t)x(t)+c(t)x′(t-τ1(t))+q(t,x(t),x(t-τ2(t)))is considered. By using fixed point theory, we give some new conditions to ensure that the zero solution is globally asymptotically stable in C1. By weakening the assumptions on the neutral coefficient c and the delay τ1 and by obtaining more manageable criteria, some existing results are improved and generalized.