Abstract and Applied Analysis
Volume 2009 (2009), Article ID 289596, 8 pages
doi:10.1155/2009/289596

Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions

Abstract

Let L denote the operator generated in L2(R+) by Sturm-Liouville equation −y′′+q(x)y=λ2y, x∈R+=[0,∞), y′(0)/y(0)=α0+α1λ+α2λ2, where q is a complex-valued function and αi∈ℂ, i=0,1,2 with α2≠0. In this article, we investigate the eigenvalues and the spectral singularities of L and obtain analogs of Naimark and Pavlov conditions for L.