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 Key Takeaways
🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
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.
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
M. Adıvar and M. Bohner, Spectral analysis of q-difference equations with spectral singularities, Math. Comput. Model. 43, 695-703, 2006
Z.S. Agranovich and V.A. Marchenko, The Inverse problem of scattering theory, Pratt Institute Brooklyn, New York, 1963
G.E. Andrews, R. Askey, R. Roy, Special functions (No. 71), Cambridge University Press, 1999
Y. Aygar and E. Bairamov, Scattering theory of impulsive Sturm–Liouville equation in quantum calculus, Bull. Malays. Math. Sci. Soc. 42, 3247-3259, 2019
Y. Aygar and M. Bohner, On the spectrum of eigenparameter-dependent quantum difference equations, Appl. Math. Inf. Sci. 9, 1725–1729, 2015
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
Y. Aygar and M. Bohner, Spectral analysis of a matrix-valued quantum-difference operator, Dyn. Syst. Appl. 25, 29-37, 2016
D.D. Bainov and P.S. Simeonov, Systems with impulse effect stability theory and applications, Ellis Horwood Limited, Chichester, 1989
D.D. Bainov and P.S. Simeonov, Impulsive differential equations: asymptotic proper- ties of the solutions, World Scientific, 1995
E. Bairamov, Y. Aygar and S. Cebesoy, Investigation of spectrum and scattering function of impulsive matrix difference operators, Filomat 33, 1301-1312, 2019
E. Bairamov, Y. Aygar and B. Eren, Scattering theory of impulsive Sturm-Liouville equations, Filomat 31, 5401-5409, 2017
E. Bairamov, Y. Aygar and D. Karslioglu, Scattering analysis and spectrum of discrete Schrödinger equations with transmission conditions, Filomat 31, 5391-5399, 2017
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
E. Bairamov, S. Cebesoy and I. Erdal, Difference equations with a point interaction, Math. Meth. Appl. Sci. 42, 5498-5508, 2019
M. Benchohra, J. Henderson and S. Ntouyas, Impulsive differential equations and inclusions, New York, Hindawi Publishing Corporation, 2006
M. Bohner and S. Cebesoy, Spectral analysis of an impulsive quantum difference op- erator, Math. Meth. Appl. Sci. 42, 5331-5339, 2019
K.M. Case, On discrete inverse scattering problems II, J. Math. Phys. 14, 916-920, 1973
K.M. Case and S.C. Chiu, The discrete version of the Marchenko equations in the inverse s