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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 503267, 7 pages
http://dx.doi.org/10.1155/2013/503267
Research Article

Green's Function Method for Self-Adjoint Realization of Boundary-Value Problems with Interior Singularities

Department of Mathematics, Faculty of Arts and Science, Gaziosmanpaşa University, 60250 Tokat, Turkey

Received 24 June 2013; Accepted 5 September 2013

Academic Editor: Ravshan Ashurov

Copyright © 2013 K. Aydemir and O. Sh. Mukhtarov. 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

The purpose of this paper is to investigate some spectral properties of Sturm-Liouville type problems with interior singularities. Some of the mathematical aspects necessary for developing our own technique are presented. By applying this technique we construct some special solutions of the homogeneous equation and present a formula and the existence conditions of Green's function. Furthermore, based on these results and introducing operator treatment in adequate Hilbert space, we derive the resolvent operator and prove self-adjointness of the considered problem.