Filomat 2022 Volume 36, Issue 18, Pages: 6279-6288
https://doi.org/10.2298/FIL2218279A
Full text (
213 KB)
A discrete boundary value problem with point interaction
Aygar Yelda (Department of Mathematics, Ankara University, Tandoğan, Ankara, Türkiye), yaygar@ankara.edu.tr
Koprubasi Turhan (Department of Mathematics, Kastamonu University, Kastamonu, Türkiye), tkoprubasi@kastamonu.edu.tr
This paper is concerned with a boundary value problem (BVP) for discrete
Sturm-Liouville equation with point interaction and boundary conditions
depending on a hyperbolic eigenvalue parameter. This paper presents some
spectral and scattering properties of this BVP in terms of Jost solution,
scattering solutions, scattering function, continuous and discrete spectrum.
In addition, the resolvent operator of the BVP is obtained to get the
properties of eigenvalues. Furthermore, an example is considered as a
special case of the main problem to demonstrate the effectiveness of our
results.
Keywords: Scattering solution, Point interaction, Eigenvalue, Resolvent operator, Scattering function
Show references
T. Y. Na, Computational Methods in Engineering Boundary Value Problems, Academic Press, New York, 1979.
G. Maise, A. J. Sabadell, Electrostatic probe measurement in solid-propellant rocket exhausts, AIAA J. 8(5) (1970) 895-901. DOI: 10.2514/3.5784.
R. P. Agarwal, D. O’Regan, Infinite interval problems modeling phenomena which arise in the theory of plasma and electrical potential theory, Stud. Appl. Math. 111 (2003) 339-358. DOI: 10.1111/1467-9590.t01-1-00237.
E. Bairamov, Y. Aygar, D. Karslioglu, Scattering analysis and spectrum of discrete Schrdinger equations with transmission conditions, Filomat 31(17) (2017) 5391-5399. DOI: 10.2298/FIL1717391B.
E. Bairamov, Y. Aygar, B. Eren, Scattering theory of impulsive Sturm-Liouville equations, Filomat 31(17) (2017) 5401-5409. DOI: 10.2298/FIL1717401B.
Y. Aygar, E. Bairamov, Scattering theory of impulsive Sturm-Liouville Equation in quantum calculus, Bull. Malys. Math. Sci. Soc. 42(6) (2019) 3247-3259. DOI: 10.1007/s40840-018-0657-2.
E. Bairamov, Y. Aygar, G. B. Oznur, Scattering properties of eigenparameter-dependent impulsive Sturm-Liouville equations, Bull. Malys. Math. Sci. Soc. 43(3) (2020) 2769-2781. DOI: 10.1007/s40840-019-00834-5.
E. Bairamov, Y. Aygar, S. Cebesoy, Investigation of spectrum and scattering function of impulsive matrix difference operators, Filomat 33(5) (2019) 1301-1312. DOI: 10.2298/FIL1905301B.
Y. Aygar Küçükevcilioğlu, E. Bairamov, G. G. Özbey, On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm-Liouville equations, Turkish J. of Math. 45(2) (2021) 988-1000. DOI: 10.3906/mat-2101-45.
E. Bairamov, S. Cebesoy, I. Erdal, Properties of eigenvalues and spectral singularities for impulsive quadratic pencil of difference operators, J. Appl. Anal. Comput. 9(4) (2019) 1454-1469. DOI: 10.11948/2156-907X.20180280.
E. Bairamov, I. Erdal, S. Yardımcı Spectral properties of an impulsive Sturm-Liouville operator, J. Inequal. Appl. Paper No. 191 (2018) 16 ppNo. 191, 16 pp. DOI: 10.1186/s13660-018-1781-0.
B. P. Allahverdiev, E. Bairamov, E. Ugurlu, Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions, J. Math. Anal. Appl. 401(1) (2013) 388-396. DOI: 10.1016/j.jmaa.2012.12.020.
A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995. DOI: 10.1142/2892.
V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics 6, World Scientific, Singapore, 1989. DOI: 10.1142/0906.
D. D. Bainov, P. S. Simeonov, Impulsive Differential Equations: Asymptotic Properties of the Solutions, World Scientific, Singapore, 1995. DOI: 10.1142/2413.
D. D. Bainov, P. S. Simeonov, Oscillation Theory of Impulsive Differential Equations, International Publications, Orlando, FL, USA, 1998.
D. D. Bainov, P. S. Simeonov, Systems with Impulse Effect Stability Theory and Applications, Ellis Horwood Limited, Chichester, 1989.
L. A. Lusternik, V. I. Sobolev, Elements of Functional Analysis, Halsted Press, New York, 1974.
I. A. Glazman, Direct Methods of Qualitative Spectral Analysis of Singular Diferential Operators, Israel Program for Scientific Translations, Jerusalem, 1965.
M. A. Naimark, Linear Differential Operators. I-II, Ungar, New York, 1968.