Sturm-Liouville问题的m-函数与谱  

On m-function and Spectra of Sturm-Liouville Problems

作　　者：傅守忠[1] 王忠[1] 

机构地区：[1]肇庆学院数学与统计学院,肇庆526061

出　　处：《应用数学学报》2015年第2期350-355,共6页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11171295;No.11171198);肇庆学院博士启动基金资助项目

摘　　要：本文先给出了Sturm-Liouville问题的Weyl-Titchmarsh m-函数对谱参数和端点的导数,进而推出其对于谱参数的分段单调性;然后利用m-函数定义了Sturm-Liouville问题的广义特征多项式,并由此得到Sturm-Liouville问题的谱对边界和参数的导数的一个简短证明.In this paper, some properties of Weyl-Titchmarsh m-function of Sturm-Liouville problems and an application of them were discussed. Firstly, we give the derivatives of Weyl-Titchmarsh m-function of Sturm-Liouville problems for the spectral parameter and end-points, and have that m-function is a piecewise monotone increasing function for the spectral parameter on the real axis. Then we defined the generalized characteristic func- tion of Sturm-Liouville Problems by using the Weyl-Titchmarsh m-function, and provide a short proof for the eigenvalues of Sturm-Liouville problems depend continuously on the the end-points and the boundary conditions by using generalized characteristic furtction.

关 键 词：特征值 逆问题 Sturm—Liouville算子 

分 类 号：O175.3[理学—数学]