Dependence of eigenvalue of Sturm-Liouville problem with singular potential and eigenparameter-dependent boundary conditions(边界条件含有谱参数的奇异Sturm-Liouville算子特征值的依赖性)

In this paper, we study the dependence of eigenvalue of Sturm-Liouville operator with distributed potential function and prove the continuous dependence of eigenvalue branch by establishing boundary condition space and constructing embedded mapping. Moreover, in the sense of Fréchet derivative, the differential expressions of eigenvalue branches with respect to all given parameters are obtained.研究了一类具有分布势函数的 Sturm-Liouville算子特征值的依赖性。通过建立边界条件空间，构造嵌入映射，证明了特征值分支的连续依赖性，并且在 Fréchet导数意义下，获得了特征值分支关于所有参数的微分表达式。