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

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.