In this paper, we consider the operator L generated in L2 (R+) by the Sturm-Liouville equation (formula presented), and the boundary condition (formula presented), where q is a complex-valued function, (formula presented) is an eigenparameter. Under the conditions(formula presented), using the uniqueness theorems of analytic functions, we prove that L has a finite number of eigenvalues and spectral singularities with finite multiplicities.