Some Spectral And Scattering Properties of Generalized Eigenparameter Dependent Discrete Transmission Sturm-Liouville Equation

Özbey G. G., ÖZNUR G. B., AYGAR KÜÇÜKEVCİLİOĞLU Y., KÖPRÜBAŞI T.

Honam Mathematical Journal, cilt.45, ss.457-470, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2023
  • Doi Numarası: 10.5831/hmj.2023.45.3.457
  • Dergi Adı: Honam Mathematical Journal
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.457-470
  • Gazi Üniversitesi Adresli: Evet

Özet

In this study, we set a boundary value problem (BVP) consisting of a discrete Sturm-Liouville equation with transmission condition and boundary conditions depending on generalized eigenvalue parameter. Discussing the Jost and scattering solutions of this BVP, we present scattering function and find some properties of this function. Furthermore, we obtain resolvent operator, continuous and discrete spectrum of this problem and we give an valuable asymptotic equation to get the properties of eigenvalues. Finally, we give an example to compare our results with other studies.