Dergiler / Hacettepe Journal of Mathematics and Statistics / 2022 / Cilt: 51 - Sayı: 1

Scattering analysis of a quantum impulsive boundary value problem with spectral parameter

Sayfa
142–155
Yayın Tarihi
2022-02-14
DOI
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Furthermore, we discuss asymptotic behavior of the Jost solution and properties of eigenvalues.Also, we illustrate our results by a detailed example which is the special case of main problem.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We are interested in scattering and spectral analysis of an impulsive boundary value problem (IBVP) generated with a $q$-difference equation with eigenparameter in boundary condition in addition to impulsive conditions.
📊
Temel Bulgular & Veri:We work on the Jost solution and scattering function of this problem, and by using the scattering solutions, we establish the resolvent operator, continuous spectrum and point spectrum of this problem.
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Sonuç & Katkı:Furthermore, we discuss asymptotic behavior of the Jost solution and properties of eigenvalues.Also, we illustrate our results by a detailed example which is the special case of main problem.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:q-difference equation · impulsive condition · scattering solution

Abstract

We are interested in scattering and spectral analysis of an impulsive boundary value problem (IBVP) generated with a $q$-difference equation with eigenparameter in boundary condition in addition to impulsive conditions. We work on the Jost solution and scattering function of this problem, and by using the scattering solutions, we establish the resolvent operator, continuous spectrum and point spectrum of this problem. Furthermore, we discuss asymptotic behavior of the Jost solution and properties of eigenvalues.Also, we illustrate our results by a detailed example which is the special case of main problem.

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Bu Makaleye Atıf Yap

AYGAR, Y., ÖZBEY, G. G. (2022). Scattering analysis of a quantum impulsive boundary value problem with spectral parameter. Hacettepe Journal of Mathematics and Statistics, Cilt: 51 - Sayı: 1, 142–155. https://ajindex.com/articles/669246

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Kaynakça (18)

  1. M. Adıvar and M. Bohner, Spectral analysis of q-difference equations with spectral singularities, Math. Comput. Model. 43, 695-703, 2006
  2. Z.S. Agranovich and V.A. Marchenko, The Inverse problem of scattering theory, Pratt Institute Brooklyn, New York, 1963
  3. G.E. Andrews, R. Askey, R. Roy, Special functions (No. 71), Cambridge University Press, 1999
  4. Y. Aygar and E. Bairamov, Scattering theory of impulsive Sturm–Liouville equation in quantum calculus, Bull. Malays. Math. Sci. Soc. 42, 3247-3259, 2019
  5. Y. Aygar and M. Bohner, On the spectrum of eigenparameter-dependent quantum difference equations, Appl. Math. Inf. Sci. 9, 1725–1729, 2015
  6. Y. Aygar and M. Bohner, A polynomial-type Jost solution and spectral properties of a self-adjoint quantum-difference operator, Complex Anal. Oper. Theory 10, 1171– 1180, 2016
  7. Y. Aygar and M. Bohner, Spectral analysis of a matrix-valued quantum-difference operator, Dyn. Syst. Appl. 25, 29-37, 2016
  8. D.D. Bainov and P.S. Simeonov, Systems with impulse effect stability theory and applications, Ellis Horwood Limited, Chichester, 1989
  9. D.D. Bainov and P.S. Simeonov, Impulsive differential equations: asymptotic proper- ties of the solutions, World Scientific, 1995
  10. E. Bairamov, Y. Aygar and S. Cebesoy, Investigation of spectrum and scattering function of impulsive matrix difference operators, Filomat 33, 1301-1312, 2019
  11. E. Bairamov, Y. Aygar and B. Eren, Scattering theory of impulsive Sturm-Liouville equations, Filomat 31, 5401-5409, 2017
  12. E. Bairamov, Y. Aygar and D. Karslioglu, Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions, Filomat 31, 5391-5399, 2017
  13. E. Bairamov, Y. Aygar and G.B. Oznur, Scattering Properties of Eigenparameter- Dependent Impulsive Sturm–Liouville Equations, Bull. Malays. Math. Sci. Soc. 43, 2769-2781, 2020
  14. E. Bairamov, S. Cebesoy and I. Erdal, Difference equations with a point interaction, Math. Meth. Appl. Sci. 42, 5498-5508, 2019
  15. M. Benchohra, J. Henderson and S. Ntouyas, Impulsive differential equations and inclusions, New York, Hindawi Publishing Corporation, 2006
  16. M. Bohner and S. Cebesoy, Spectral analysis of an impulsive quantum difference op- erator, Math. Meth. Appl. Sci. 42, 5331-5339, 2019
  17. K.M. Case, On discrete inverse scattering problems II, J. Math. Phys. 14, 916-920, 1973
  18. K.M. Case and S.C. Chiu, The discrete version of the Marchenko equations in the inverse s