李雅普诺夫非线性微分方程零解的稳定性定理的推广(英文)

The Generalization of the Stability Theorem of the Null Solution for Liapunov's Nonlinear Differential Equation

研究了如下非线性微分方程x′=A(t)x+f(t,x),利用指数型二分性理论和李雅普诺夫第二方法,得到了上述扰动系统在一定的条件下能和其线性系统保持同步的稳定性,推广了现有的相关理论。

The nonlinear differential equation x^1=A （t）x＋f（t ,x） where A （t） ∈ C（R＋,R^n）, is studied in this paper. By using theories of the exponential dichotomy and second method of Liapunov, we obtain the stability that the above perturbed system synchronizes with its linear system under some given conditions. Our results generalize and improve the existed corresponding theories.