Dependence of Eigenvalues of Sturm–Liouville Problems with Eigenparameter-Dependent Boundary Conditions and Interface Conditions

In this paper, regular Sturm–Liouville problems with eigenparameter-dependent boundary conditions and interface conditions are investigated. We obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problem: the coefficients, the boundary conditions, the interface conditions, as well as the endpoints. Moreover, we find the differential expressions for each parameters, respectively.