This work is devoted to discuss some spectral properties and the scattering function of the impulsive operator generated by the Sturm–Liouville equation. We present a different method to investigate the spectral singularities and eigenvalues of the mentioned operator. We also obtain the finiteness of eigenvalues and spectral singularities with finite multiplicities under some certain conditions. Finally, we illustrate our results by a detailed example.
In this work, we are concerned with di¤erence operator of second order with impulsive condition. By the help of a transfer matrix M , we present scattering function of corresponding operator and examine the spectral properties of this impulsive problem.
In this paper, we consider an impulsive second‐order difference equation on the whole axis. We determine eigenvalues, spectral singularities, continuous spectrum corresponding to this difference equation with an impulsive condition by using the asymptotic properties of Jost functions, and uniqueness theorems of analytic functions. Finally, we demonstrate that the impulsive difference equation has finite number of eigenvalues and spectral singularities with finite multiplicities under certain conditions.
The objective of this work is to investigate some spectral properties of an impulsive Sturm-Liouville boundary value problem on the semi axis. By the help of analytical properties of the Jost solution and asymptotic properties of a transfer matrix M , we examine the existence of the spectral singularities and eigenvalues of the impulsive operator generated by the Sturm-Liouville equation.
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