非线性时滞微分方程零解的全局渐近稳定性

Global asymptotic stability of zero solutions to nonlinear differential equation with delays

利用Banach不动点方法,研究非线性时滞微分方程在C1空间上零解的全局渐近稳定性.之前,几乎所有学者在研究非线性时滞微分方程零解稳定性时,都要求中立项系数c可微和时滞τ2二次可微,且τ2′≠1.与大多数学者研究的方法不相同,所得定理仅要求c和τ2连续,推广和改进了前人研究的结果,并给出了一个例子说明结论的有效性.

By using the fixed point theory,the strict theorem for the global asymptotic stability of zero solutions of nonlinear differential equations with delays in C^1 is studied.Before,almost all scholars studied the stability of zero solutions of nonlinear differential equations with delay,they required that the neutral coefficient c be differentiable and the delayτ2 quadratic differentiable,andτ2′≠1.Unlike the methods studied by most scholars,the obtained theorem only requires c andτ2 to be Continuous.In addition,the results of previous studies are generalized and improved,an example is given to illustrate the validity of the conclusions.