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

Let denote the operator generated in 2(ℛ+) by the Sturm-Liouville problem: −+()=2, ∈ℛ+=[0,∞), (/)(0)=(1+0)/(1+0), where is a complex valued function and 0,1,0,1∈, with 01−10≠0. In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of . In particular, we obtain the conditions on under which the operator has a finite number of the eigenvalues and the spectral singularities