时标线性加权Sturm-Liouville特征值问题的谱理论分析

Spectral Theory of Linear Weighted Sturm-Liouville Eigenvalue Problems

对一类时标线性加权Sturm-Liouville特征值问题,获得了与特征值和特征函数的广义零点分布有关的一些全局结果,建立了Sturm比较定理和Sturm分离定理,同时证明了第一个正特征值和对应正特征函数的存在性.

This paper discusses some global results on eigenvalue and zero distribution for eigenfunction of the linear weighted Sturm-Liouville eigenvalue problem on time scales. We obtain Sturm comparison theorem and Sturm separation theorem and prove the existence of the smallest positive eigenvalue and the corresponding positive eigenfunction.