一类微分方程组特征值的研究

Study on the Eigenvalues for a Differential Equations Multi-agent System

微分方程组的特征值问题是数学学科的一个重要内容,在力学和物理学等领域有着广泛的应用。将一类特殊的常微分方程组推广到此类方程组普遍存在的形式,并研究其第n个特征值和第n+1个特征值之间的关系,得到了两者的关系定理。在研究中用到了分部积分法,Schwartz不等式及Rayleigh定理等重要方法和定理,为同类问题的研究提供了参考。

It is an important content of mathematics to study the eigenvalue problem of differential equations,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 equations to its general form of ordinary differential equations, This paper studies the relationship between the nth eigenvalue and the(n+1)th eigenvalue of the equations, 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.