Spectral Properties of Discrete Klein–Gordon s-Wave Equation with Quadratic Eigenparameter-Dependent Boundary Condition

  • Nihal YokusEmail author
  • Nimet Coskun
Research Paper
Part of the following topical collections:
  1. Mathematics
  2. Mathematics
  3. Mathematics
  4. Mathematics


In this study, we consider the spectral analysis of the boundary value problem (BVP) consisting of the discrete Klein–Gordon equation and the quadratic eigenparameter-dependent boundary condition. Presenting the Jost solution and Green’s function, we investigate the finiteness and other spectral properties of the eigenvalues and spectral singularities of this BVP under certain conditions.


Eigenparameter Spectral analysis Eigenvalues Spectral singularities Discrete equation Klein–Gordon equation 



The authors would like to express their thanks to the reviewers for their helpful comments and suggestions.


  1. Adıvar M (2010) Quadratic pencil of difference equations: Jost solutions, spectrum, and principal vectors. Quaest Math 33(3):305–323MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bairamov E (2004) Spectral properties of the nonhomogeneous Klein–Gordon s-wave equations. Rocky Mt J Math 34:1–11MathSciNetCrossRefzbMATHGoogle Scholar
  3. Bairamov E, Coskun C (2005) The structure of the spectrum of a system of difference equations. Appl Math Lett 18(4):387–394MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bairamov E, Yokus N (2009) Spectral singularities of Sturm-Liouville problems with eigenvalue-dependent boundary conditions. Abstr Appl Anal. MathSciNetzbMATHGoogle Scholar
  5. Bairamov E, Çakar Ö, Celebi AO (1997) Quadratic pencil of schrödinger operators with spectral singularities: discrete spectrum and principal functions. J Math Anal Appl 216(1):303–320MathSciNetCrossRefzbMATHGoogle Scholar
  6. Degasperis A (1970) On the inverse problem for the Klein–Gordon s-wave equation. J Math Phys 11(2):551–567MathSciNetCrossRefGoogle Scholar
  7. Dolzhenko EP (1979) Boundary-value uniqueness theorems for analytic functions. Math Notes Acad Sci USSR 25(6):437–442zbMATHGoogle Scholar
  8. Kir E, Bascanbaz-Tunca G, Yanik C (2005) Spectral properties of a non selfadjoint system of differential equations with a spectral parameter in the boundary condition. Proyecciones (Antofagasta) 24(1):49–63MathSciNetCrossRefzbMATHGoogle Scholar
  9. Koprubasi T (2014) Spectrum of the quadratic eigenparameter dependent discrete Dirac equations. Adv Differ Equ 2014(1):148MathSciNetCrossRefzbMATHGoogle Scholar
  10. Koprubasi T, Yokus N (2014) Quadratic eigenparameter dependent discrete Sturm–Liouville equations with spectral singularities. Appl Math Comput 244:57–62MathSciNetzbMATHGoogle Scholar
  11. Levitan BM, Sargsjan IS (1991) Sturm–Liouville and Dirac operators. Translated from the Russian mathematics and its applications (Soviet series), vol. 59Google Scholar
  12. Naimark MA (1960) Investigation of the spectrum and the expansion in eigenfunctions of a nonselfadjoint differential operator of the second order on a semi-axis. Am Math Soc Transl 2(16):103–193Google Scholar
  13. Naimark MA (1968) Linear differential operators: part II: linear differential operators in Hilbert space with additional material by the author. F. Ungar Publishing Company, New YorkzbMATHGoogle Scholar
  14. Pavlov BS (1967) The non-self-adjoint schrodinger operator I, II, III, topics in math. Phys Consult Bur NY 1968:1969Google Scholar

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© Shiraz University 2019

Authors and Affiliations

  1. 1.Department of MathematicsKaramanoglu Mehmetbey UniversityKaramanTurkey

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