齐线性微分方程非零解的零点个数定理  

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

作　　者：樊树芳[1] 孙丙虎[2] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059 [2]聊城一中,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2009年第4期13-15,共3页Journal of Liaocheng University:Natural Science Edition

摘　　要：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.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.

关 键 词：齐线性微分方程 非零解 零点 

分 类 号：O175.1[理学—数学]