On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm-Liouville equations

AYGAR KÜÇÜKEVCİLİOĞLU Y., Bairamov E., Ozbey G. G.

TURKISH JOURNAL OF MATHEMATICS, vol.45, no.2, pp.988-1000, 2021 (SCI-Expanded, Scopus, TRDizin) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.3906/mat-2101-45
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.988-1000
  • Keywords: Impulsive condition, discrete Sturm?Liouville equation, spectral parameter, eigenvalue, resolvent operator, scattering solution, scattering function, BOUNDARY-VALUE-PROBLEMS, PULSE VACCINATION, CONTROLLABILITY
  • Ankara University Affiliated: Yes

Abstract

This work develops scattering and spectral analysis of a discrete impulsive Sturm?Liouville equation with spectral parameter in boundary condition. Giving the Jost solution and scattering solutions of this problem, we find scattering function of the problem. Discussing the properties of scattering function, scattering solutions, and asymptotic behavior of the Jost solution, we find the Green function, resolvent operator, continuous and point spectrum of the problem. Finally, we give an example in which the main results are made explicit.