具有转移条件且边界条件中含有多项式谱参数的Sturm-Liouville问题的有限谱  

Finite Spectrum of Sturm-Liouville Problems with Transmission Condition and Polynomial Parameter Boundary Condition

作　　者：朱军伟 顾丽娜 ZHU Jun-wei;GU Li-na(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学理学院

出　　处：《兰州文理学院学报（自然科学版）》2019年第6期7-11,57,共6页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：主要研究下述具有转移条件且边界条件中含有多项式谱参数的Sturm-Liouville问题{-(py′)′+qy=λwy,AλY(a)+BλY(b)=0,C Y(c-)+D Y(c+)=0.通过构造判断函数证明了这类问题具有有限谱并且所有谱都是特征值,最后通过举例进一步论证.运用的主要工具是判断函数的迭代.In this paper,the following finite spectrum of Sturm-Liouville problems with transmission condition and polynomial parameter boundary condition were studied {-(py′)′+qy=λwy,AλY(a)+BλY(b)=0,CY(c-)+DY(c+)=0.By constructing the characteristic function,it was proved that this kind of problems had finite spectrums and all the spectrums consisted of eigenvalues.The main tool used in this paper was the iterative construction of discriminant function.

关 键 词：STURM-LIOUVILLE问题 多项式谱参数 判断函数 

分 类 号：O175[理学—数学]