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

Abstract EN

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.