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

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

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.