一阶常微分方程比较定理的高阶推广

The Extent of Comparison Theorems of Ordinary Differential Equations to the Higher Order

比较定理是研究常微分方程解的属性的基本工具。但对于高阶的情况,现有的结论只给出了类似把解作为向量范数之间的比较。我们将一阶常微分方程的比较定理推广到高阶,从而给出了高阶常微分方程的解自身的大小的比较定理。

The comparison theorem for the ordinary differential equation is the basic tool to study the relevant solution＇s properties. However, in the higher order case, what we have now is only the theorem in comparing norms of the solutions. Therefore, we extend the comparison theorem to the higher order so that we can compare the solutions directly.