Abstract and Applied Analysis
Volume 2010 (2010), Article ID 982749, 10 pages
doi:10.1155/2010/982749
Research Article

Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter

Elgiz Bairamov1 and M. Seyyit Seyyidoglu2

1Department of Mathematics, Science Faculty, Ankara University, 06100 Ankara, Turkey
2Department of Mathematics, Science and Art Faculty, Usak University, 64200 Campus-Uşak, Turkey

Received 6 December 2009; Accepted 16 February 2010

Academic Editor: Ağacik Zafer

Copyright © 2010 Elgiz Bairamov and M. Seyyit Seyyidoglu. 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

Let A denote the operator generated in L2(R+) by the Sturm-Liouville problem: -y′′+q(x)y=λ2y, x∈R+=[0,∞), (y′/y)(0)=(β1λ+β0)/(α1λ+α0), where q is a complex valued function and α0,α1,β0,β1∈C, with α0β1-α1β0≠0. In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of A. In particular, we obtain the conditions on q under which the operator A has a finite number of the eigenvalues and the spectral singularities.