Asymptotic Stability Of Delay Differential Equations

In this paper, we take attention to the stability of the n-dimensional nonautonomous equation x’(t)=-A(t)x(t)+B(t)F(xt) by applying fixed point theory. We establish the sufficient, necessary, and sufficient and necessary criteria for the asymptotic stability of the equation by applying fixed point theory. The technique is the contractive mapping principle. At last, the criteria is applied to obtain the stability of some examples, and the numerical simulations also illustrate the theoretical results.