Eigenvalues of Sturm-Liouville problems with distributional potentials and eigenparameter-dependent boundary conditions

Abstract

In this paper, regular Sturm-Liouville problems with distributional potentials and eigenparameter-dependent boundary 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, and the endpoints, in particular, the eigenparameter-dependent boundary condition matrix. Moreover, we find the differential expressions for each parameters.

Mathematics Subject Classification (2020):

• Primary: 34L10
• 34B20
• Secondary: 47A45

Key words:

• Sturm-Liouville problems
• distributional potentials
• eigenparameter-dependent boundary conditions
• eigenvalues