Spectral Singularities of Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions

Abstract EN

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 ofNaimark and Pavlov conditions for L.