本项目主要研究具有测度系数的Sturm-Liouville算子的谱性质。首先，利用Prufer变换以及基本解关于参数λ的渐近性质，得到不同类型的自伴边界条件下特征值之间的关系。通过引入恰当的拓扑空间，研究特征值关于算子系数以及边界条件的依赖性， 所得结果将推广经典Sturm-Liouville理论的相关结论。此外，我们还将利用具有测度系数的Sturm-Liouville算子研究一类度量图上具有δ型条件以及δ'型条件的Schrödinger算子，推广Glazman-Povzner-Wienholtz定理，并且基于二次型理论以及空间分解，给出算子谱纯离散的判定准则。

This paper deals with the spectral properties of the Sturm-Liouville operators with measure-valued coefficients. Firstly, we discuss the relationships of the eigenvalues under different boundary conditions on the basis of the Prufer transformation and the asymptotic properties of the fundamental solutions on the parameter λ. Then, by introducing a proper topological space, we also pay particular attention to the dependence of the eigenvalues on the coefficients of the operators and the boundary conditions. These investigations will extend the results in the classical Sturm-Liouville theory. Moreover, Schrödinger operators with δ and δ' type conditions on metric graph will be researched by means of the Sturm-Liouville operators with measure-valued coefficients, Glazman-Povzner-Wienholtz theorem will be extended in our research, and then the discreteness of the spectrum will be studied by utilizing the form approach and the basic decomposition of the function space.