Finite spectrum of Sturm-Liouville problems with eigenparameter-dependent boundary conditions on time scales

Abstract

The spectral analysis of a class of Sturm-Liouville problems with eigenparameter-dependent boundary conditions on bounded time scales is investigated. By partitioning the bounded time scale such that the
coefficients of Sturm-Liouville equation satisfy some certain conditions on the adjacent subintervals, the finite eigenvalue results are obtained. The results show that the number of eigenvalues not only depend on the partition of the bounded time scale, but also depend on the eigenparameter-dependent boundary conditions. Both the self-adjoint and the non-self-adjoint cases are considered.