Table of Contents
Physics Research International
Volume 2013, Article ID 159243, 9 pages
Research Article

A Sturm-Liouville Problem with a Discontinuous Coefficient and Containing an Eigenparameter in the Boundary Condition

1Department of Mathematics, Faculty of Arts and Science, Namik Kemal University, 59030 Tekirdağ, Turkey
2Department of Mathematics Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey

Received 10 April 2013; Accepted 18 July 2013

Academic Editor: Ashok Chatterjee

Copyright © 2013 Erdoğan Şen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study a Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We give an operator-theoretic formulation, construct fundamental solutions, investigate some properties of the eigenvalues and corresponding eigenfunctions of the discontinuous Sturm-Liouville problem and then obtain asymptotic formulas for the eigenvalues and eigenfunctions and find Green function of the discontinuous Sturm-Liouville problem.