齐线性微分方程非零解的零点个数定理

对于高阶的变系数齐线性微分方程，我们没有统一的方法可以求出其所有非零解的函数表达式，因此从宏观上研究其非零解的性质是非常必要的．本文基于常微分方程解的存在唯一性定理，讨论了各阶齐线性微分方程非零解的一个重要性质，就是其非零解在有限闭区间上的零点个数至多为有限个．

On the Number of Zeros for Non-zero Solutions of Linear Homogeneous Differential Equation

For the high-order linear homogeneous differential equations with variable coefficients, there has no unified way to get the functional expression of their non-zero solutions, so it is very necessary to study the property of non-zero solutions macroscopicalty. Here based on the existence and uniqueness theorem of solutions for ordinary differential equation, an important property of non-zero solutions of all order linear homogeneous differential equations is diseussed, that is the limited propery of the zeros number of the non-zero solutions on the closed interval.