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<p>We handle an impulsive Sturm–Liouville boundary value problem on semi axis. The difference between this study and other works in the literature is that the boundary condition is dependent on a generalized parameter. This adds a unique perspective to the examination of the scattering theory and spectral analysis of the problem. Firstly, we find Jost solution, resolvent operator and Green function of the impulsive Sturm–Liouville boundary value problem. Furthermore, we investigate the sets of eigenvalues and spectral singularities of this problem. Finally, we get Jost function and scattering, and we investigate the properties of scattering function of this impulsive Sturm–Lioville problem.</p>

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Spectral Properties of Generalized Eigenparameter Dependent Impulsive Sturm–Liouville Equation

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Güler Başak Öznur

摘要

We handle an impulsive Sturm–Liouville boundary value problem on semi axis. The difference between this study and other works in the literature is that the boundary condition is dependent on a generalized parameter. This adds a unique perspective to the examination of the scattering theory and spectral analysis of the problem. Firstly, we find Jost solution, resolvent operator and Green function of the impulsive Sturm–Liouville boundary value problem. Furthermore, we investigate the sets of eigenvalues and spectral singularities of this problem. Finally, we get Jost function and scattering, and we investigate the properties of scattering function of this impulsive Sturm–Lioville problem.