A Discrete Boundary Value Problem with Point Interaction

AYGAR KÜÇÜKEVCİLİOĞLU Y., Koprubasi T.

FILOMAT, vol.36, no.18, pp.6279-6288, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 18
  • Publication Date: 2022
  • Doi Number: 10.2298/fil2218279a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.6279-6288
  • Ankara University Affiliated: Yes

Abstract

This paper is concerned with a boundary value problem (BVP) for discrete Sturm-Liouville equation with point interaction and boundary conditions depending on a hyperbolic eigenvalue parameter. This paper presents some spectral and scattering properties of this BVP in terms of Jost solution, scattering solutions, scattering function, continuous and discrete spectrum. In addition, the resolvent operator of the BVP is obtained to get the properties of eigenvalues. Furthermore, an example is considered as a special case of the main problem to demonstrate the effectiveness of our results.