Sturm-Liouville边值问题的特征值与特征函数

The Eigenvalues and Eigenfunctions of the Sturm-Liouville Boundary Value Problem

本文采用二阶张量和常微分算子的特征值与特征向量(函数)的研究方法,研究了Sturm-Liouville边值问题.通过这些研究得到,Sturm-Liouville系统特征值问题的微分算子是自伴的,并且其单位正交特征函数系(基)构成完备正交系(基).

This paper uses the research methods of a second order tensor and the differential operator eigenvalue and eigenvector（ functions） to study Sturm-Liouville boundary value problem. We can find that differential operator of Sturm-Liouville system eigenvalue problem is self-adjoint and its unit-orthogonal characteristic function system（ base） constitutes a complete orthogonal system（ base）.