Journal of Applied Mathematics
Volume 2013 (2013), Article ID 306917, 8 pages
http://dx.doi.org/10.1155/2013/306917
Research Article
Asymptotic Behaviour of Eigenvalues and Eigenfunctions of a Sturm-Liouville Problem with Retarded Argument
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
3Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea
4Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey
Received 18 November 2012; Accepted 1 March 2013
Academic Editor: Suh-Yuh Yang
Copyright © 2013 Erdoğan Şen et al. 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.
Abstract
In the present paper, a discontinuous boundary-value problem with retarded argument at the two points of discontinuities is investigated. We obtained asymptotic formulas for the eigenvalues and eigenfunctions. This is the first work containing two discontinuities points in the theory of differential equations with retarded argument. In that special case the transmission coefficients and retarded argument in the results obtained in this work coincide with corresponding results in the classical Sturm-Liouville operator.