Spectral Characteristics of Impulsive Schrödinger Equations With Boundary Spectral Parameter

ABSTRACT In this paper, we investigate the spectral properties of an impulsive Schrödinger equation under an impulsive condition. First, we find the Jost solution and some special solutions of the problem. Using these solutions, we give the resolvent operator of the impulsive problem. Second, we present some asymptotic equations to get the spectral properties. Then, we find the sets of eigenvalues and spectral singularities of the problem. Finally, we investigate the characteristics of eigenvalues and spectral singularities.