变时滞非线性中立型微分方程的稳定性

Stability of nonlinear neutral differential equations with variable delays

利用Banach不动点定理,研究变时滞非线性中立型微分方程,并在一定的条件下构造适当的压缩映射,得到了方程零解渐近稳定的新条件.之前,几乎所有的学者在利用Banach不动点定理研究变时滞非线性中立型微分方程时,都需要时滞τ二次可微且τ’≠1.和大多数研究方法不相同,这些新条件不需要时滞τ二次可微,也不要求τ’≠1.所得结论推广了已有文献中的相应结果,并给出了一个实例验证了所得结论的有效性.

By using the fixed point theory, the nonlinear neutral differential equation with variable delays is studied, and appropriate contractive mappings are constructed under certain conditions. New conditions for asymptotic stability of zero solutions of the equation are obtained. Previously, almost all scholars used Banach fixed point theory to study nonlinear neutral differential equations with variable delays, requiring τ quadratic differentiability and τ’≠1. Unlike most research methods, these conditions do not require a quadratic differentiability of delay τ andτ’≠1. The results obtained generalize the corresponding results in the literature. A practical example is given to verify the validity of the conclusions.