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Journals / Gazi University Journal of Science / 2021 / Volume: 34 Issue: 4

Scattering Function and The Resolvent of The Impulsive Boundary Value Problem

Elgiz Bayram(ANKARA UNIVERSITY)0000-0003-2075-5016
Güler Başak Öznur(GAZİ ÜNİVERSİTESİ)0000-0003-4130-5348
Pages
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Publication Date
2021-12-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we study scattering solutions and scattering function of an unperturbated impulsive equation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The purpose of this study is to examine the properties of scattering solutions and the scattering function of an impulsive Sturm-Liouville boundary value problem on the semi axis.
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Key Findings & Data:By using Jost solutions, we obtain the scattering function, asymptotic representation of Jost function and resolvent operator.
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Conclusion & Impact:Finally, we study scattering solutions and scattering function of an unperturbated impulsive equation.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Boundary value problem · Density function · Impulsive condition

Abstract

The purpose of this study is to examine the properties of scattering solutions and the scattering function of an impulsive Sturm-Liouville boundary value problem on the semi axis. By using Jost solutions, we obtain the scattering function, asymptotic representation of Jost function and resolvent operator. Finally, we study scattering solutions and scattering function of an unperturbated impulsive equation.

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Cite This Article

Bayram, E., Öznur, G. B. (2021). Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. Gazi University Journal of Science, Volume: 34 Issue: 4. https://doi.org/10.35378/gujs.796894

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References (11)

  1. Referans1: Naimark, M.A., “Investigation of the spectrum and the expansion in eigenfunctions of a non-self adjoint differential operators of the second order on a semi axis”, Amer. Math. Soc. Transl., 16(2):103-193, (1960).
  2. Referans2:Levitan, B.M., Sargsjan, I.J., “Sturm-Liouville and Dirac operators”, Kluwer Academic Publishers Group, Dordrecht, (1991). Referans3: Schwartz, J., “Some non-self adjoint operators”, Comm. Pure Appl. Math. 13:609-639, (1960). Referans4: Pavlov, B.S., “On the spectral theoy of non-self adjoint differential operators”, Dokl. Akad. Nauk SSSR., 146:1267-1270, (1962).
  3. Referans5: Guseinov, G.S., “On the concept of spectral singularities”, Pramana, J. Phys., 73(3):587-603, (2009).
  4. Referans6: Allahverdiev, B.P., Bairamov, E., Ugurlu, E., “Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions”, J. Math. Anal. Appl. 401(1):388-396, (2013).
  5. Referans7:Bairamov, E., Aygar, Y., Eren B., “Scattering theory of impulsive Sturm-Liouville equations”, Filomat, 31(17):5401-5409, (2017).
  6. Referans8: Guseinov, G.S., “Boundary value problems for nonlinear impulsive Hamilton systems”, J. Comput. Appl. Math., 259:780-789, (2014).
  7. Referans9:Bairamov, E., Aygar Y., Oznur, G.B., “Scattering properties of eigenparameter-dependent impulsive Sturm-Liouville equations”, Bull. Malays. Math. Sci. Soc. 43:2769-2781, (2020).
  8. Referans10: Mukhtarov, F.S., Aydemir, K., Mukhtarov, O.Sh., “Spectral analysis of one boundary value-transmission problem by means of Green’s function”, Electron. J. Math. Anal. Appl. 2:23-30, (2014). Referans11: Milman, V.D., Myshkis, A.D., “On the stability of motion in the presence of impulses”, Sib. Math. J., 1:233-237, (1960).
  9. Referans12: Perestyuk, N.A., Plotnikov, V.A., Samoilenko, A.M., Sikripnik, N.V., “Differential equations with impulse effects: Multivaled right-hand sides with discontinuities”, De Gruyter Studies in Mathematics 40, Germany, (2011).
  10. Referans13: Perestyuk, N.A., Samoilenko, A.M., Stanzhitsii, “On the existence of periodic solutions of some classes of systems of differential equations with random impulse action” Ukrain. Math. Zh. 53:1061-1079, (2001).
  11. Referans14: Samoilenka, A.M., Perestyuk, N.A., “Impulsive differential equations”, World Scientific, Singapore, (1995). Referans15: Ugurlu, E., Bairamov, E., “Spectral analysis of eigenparameter dependent boundary value transmission problems”, J. Math. Anal. Appl. 413(1):482-494, (2014).