Non-self-adjoint singular sturm-liouville problems with boundary conditions dependent on the eigenparameter

Let A denote the operator generated in L2 (R+) by the Sturm-Liouville problem: - y? + q (x) y = ?2 y, x ? R+ = [ 0,? ), (y? / y) (0) = ( ?1? + ?0) / ( ?1? + ?0), where q is a complex valued function and ?0, ?1, ?0, ?1 ?C, with ?0 ?1 -?1 ?0? 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. © 2010 E. Bairamov and M. S. Seyyidoglu