Spectral singularities of sturm-liouville problems with eigenvalue-dependent boundary conditions

Let L denote the operator generated in L 2 (R +) by Sturm-Liouville equation - y + q (x) y = λ 2 y, x R + = [ 0, ∞), y ′ (0) / y (0) = 0 + 1 λ + 2 λ 2, where q is a complex-valued function and i , i = 0, 1, 2 with 2 0. In this article, we investigate the eigenvalues and the spectral singularities of L and obtain analogs of Naimark and Pavlov conditions for L.