# 高阶线性常微分方程零点稳定性的直接判定法Direct Method of Stability of Null Solution for Higher Order Ordinary Differential Equations

Abstract: “Higher order ordinary differential equations can always be transformed to be first order ordinary differential systems”. By this fact, we proved that higher order ordinary differential equation and first order ordinary differential system transformed from it have the same characteristic roots. Then, by Lyapunov Theorem, we show that the stability of null solution of higher order ordinary differential equation can be determined by its characteristic roots.

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[3] Perko, L. (2001) Differential Questions and Dynamical Systems. 3rd Edition, Sprin-ger-Verlag, Berlin Heidelberg.
http://dx.doi.org/10.1007/978-1-4613-0003-8

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