Eigenvalues of sturm-liouville problems with distribution potentials on time scales

Abstract

The eigenvalues of a class of Sturm-Liouville problems with distribution potentials and eigenparameter-dependent boundary conditions on bounded time scales are investigated. By treating with the eigenparameter-dependent boundary condition, the governing equation with distribution potential and time scales, the results of finite number of eigenvalues are obtained. The results show that the number of eigenvalues depend on the partition of time scale and the eigenparameterdependent boundary conditions given, but is independent on the distribution potentials.

Key words: Sturm-Liouville problems, time scales, distribution potentials, eigenvalues, eigenparameter-dependent boundary conditions.