一类常微分方程第二特征值的研究

Study on the Second Eigenvalues for a Differrential Equation

微分方程的特征值问题是数学学科的一个重要内容,在力学等物理领域也有着广泛的应用。本研究将一类特殊的常微分方程推广到此类方程普遍存在的形式,并研究了其第一特征值λ_(1)和第二特征值λ_(2)的关系,得到了两者的关系定理。在研究过程中用到了分部积分法、Schwartz不等式及Rayleigh定理等其他重要方法和定理,为同类问题的研究提供了参考途径。

It is an important content of mathematics to study the eigenvalue problem of differential equation,as it is also widely used in practice,such as in the fields of mechanics and physics.In this paper,we extend a special ordinary differential equation to its general form of ordinary differential equation.This paper studies the relationship between the 1st eigenvalue and the 2nd eigenvalue of the equation,and the relation theorem between them is obtained.In the research process,we use integral,Reyleigh theorem,Schwartz inequality and other important methods and theorems.It provides a reference for other similar researches.