Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter - Elgiz Bairamov; M. Seyyit Seyyidoglu (Abstract and Applied Analysis)
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.