Dependence of eigenvalues of Sturm-Liouville problems on time scales with eigenparameter-dependent boundary conditions

Abstract

In this article, we study the eigenvalue dependence of Sturm-Liouville problems on time scales with spectral parameter in the boundary conditions. We obtain that the eigenvalues not only continuously but also smoothly depend on the parameters of the problem. Moreover, the differential expressions of the eigenvalues with respect to the data are given.

Keywords

• sturm-liouville problems
• time scales
• derivative formulas
• eigenparameter-dependent boundary
• 34b08
• 34n99
• 34l05