By the help of analytical properties of the Jost solution and asymptotic properties of a transfer matrix $M$, we examine the existence of the spectral singularities and eigenvalues of the impulsive operator generated by the Sturm-Liouville equation.
📌 3 Key Takeaways
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Objective & Hypothesis:The objective of this work is to investigate some spectral properties of an impulsive Sturm-Liouville boundary value problem on the semi axis.
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Key Findings & Data:The objective of this work is to investigate some spectral properties of an impulsive Sturm-Liouville boundary value problem on the semi axis.
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Conclusion & Impact:By the help of analytical properties of the Jost solution and asymptotic properties of a transfer matrix $M$, we examine the existence of the spectral singularities and eigenvalues of the impulsive operator generated by the Sturm-Liouville equation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Sturm-Liouville operators · boundary value problems · impulsive conditions
Abstract
The objective of this work is to investigate some spectral properties of an impulsive Sturm-Liouville boundary value problem on the semi axis. By the help of analytical properties of the Jost solution and asymptotic properties of a transfer matrix $M$, we examine the existence of the spectral singularities and eigenvalues of the impulsive operator generated by the Sturm-Liouville equation.
Yardımcı, Ş., Erdal, İ. (2022). Investigation of an impulsive Sturm-Liouville operator on semi axis. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 5, 1409–1416. https://ajindex.com/articles/530153
M. Adivar and E. Bairamov, Spectral singularities of the nonhomogeneous Sturm- Liouville equations, Appl. Math. Lett. 15 (7), 825–832, 2002
B.P. Allahverdiev, E. Bairamov and E. Ugurlu, Eigenparameter dependent Sturm- Liouville problems in boundary conditions with transmission conditions, J. Math. Anal. Appl. 401 (1), 388–396, 2013
G. Başcanbaz and E. Bairamov, Discrete spectrum and principal functions of non- selfadjoint differential operator, Czechoslovak Math. J. 49 (124)(4), 689–700, 1999
D. Bainov and P. Simeonov, Oscillation theory of impulsive differential equations, International Publications, Orlando, FL, 1998
E. Bairamov and A.O. Çelebi, Spectral analysis of nonselfadjoint Schrödinger opera- tors with spectral parameter in boundary conditions, Facta Univ. Ser. Math. Inform. 13, 79–94, 1998
E. Bairamov and E. Kir, Spectral properties of a finite system of Sturm-Liouville differential operators, Indian J. Pure Appl. Math. 35 (2), 249–256, 2004
E. Bairamov, Y. Aygar and B. Eren, Scattering theory of impulsive Sturm-Liouville equations, Filomat, 31, 5401–5409, 2017
E. Bairamov, Ö Çakar and A.M. Krall, An eigenfunction expansion for a quadratic pencil of a Schrödinger operator with spectral singularities, J. Differential Equations, 151 (2), 268–289, 1999
G.Sh. Guseinov, On the concept of spectral singularities, Pramana-J. Phys. 73 (3), 587–603, 2009
H.M. Huseynov and A.H. Jamshidipour, On Jost solutions of Sturm-Liouville equa- tions with spectral parameter in discontinuity condition, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 30 (4, Mathematics), 61–68, 2010
A.M. Krall, E. Bairamov and Ö. Çakar, Spectrum and spectral singularities of a quadratic pencil of a Schrödinger operator with a general boundary condition, J. Dif- ferential Equations, 151 (2), 252–267, 1999
B.M. Levitan and I.S. Sargsyan, Sturm-Liouville and Dirac Operators, “Nauka”, Moscow, 1988
V.A. Marchenko, Sturm-Liouville operators and applications, volume 22 of Operator Theory: Advances and Applications, Birkhäuser Verlag, Basel, 1986. Translated from the Russian by A. Iacob
A. Mostafazadeh, Spectral singularities of a general point interaction, J. Phys. A. 6 (1), 47–55, 2011
A. Mostafazadeh and H. Mehri-Dehnavi, Spectral singularities, biorthonormal systems and a two-parameter family of complex point interactions, J. Phys. A. 42 (12), 125303, 1–27, 2009