Using time scales to study multi-interval Sturm-Liouville problems with interface conditions
The authors consider a Sturm-Liouville problem defined on multiple intervals with interface conditions. The existence of a sequence of eigenvalues is established and the zero counts of the associated eigenfunctions are determined. Moreover, the authors reveal the continuous and discontinuous nature of the eigenvalues on the boundary condition. The approach in this paper is different from those in the literature. The authors transfer the Sturm-Liouville problem with interface conditions to a Sturm-Liouville problem on a time scale without interface conditions and then apply the Sturm-Liouville theory for equations on time scales. In this way, the authors are able to investigate the problem from a global point of view. Consequently, the authors results cover the cases when the potential function in the equation is not strictly greater than zero and when the domain consists of an infinite number of intervals.
scientific article; zbMATH DE number 6135258