Scattering Function and The Resolvent of The Impulsive Boundary Value Problem

Elgiz BAYRAM, (Ankara Üniversitesi, Fen Fakültesi, Matematik Bölümü, Ankara, Türkiye)
Güler Başak ÖZNUR (Gazi Üniversitesi, Fen Fakültesi, Matematik Bölümü, Ankara, Türkiye)
Gazi University Journal of Science
2 0
Yıl: 2021 Cilt: 34 Sayı: 4 Sayfa Aralığı: 1077 - 1087 Metin Dili: İngilizce DOI: 10.35378/gujs.796894 İndeks Tarihi: 07-11-2022

Scattering Function and The Resolvent of The Impulsive Boundary Value Problem

Öz:
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.
Anahtar Kelime: Boundary value problem Density function Impulsive condition Resolvent operator Spectral parameter

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] 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”, American Mathematical Society Translations, 16(2): 103-193, (1960).
  • [2] Levitan, B. M., Sargsjan, I. J., “Sturm-Liouville and Dirac operators”, Kluwer Academic Publishers Group, Dordrecht, (1991).
  • [3] Schwartz, J., “Some non-self adjoint operators”, Communications on Pure and Applied Mathematics, 13: 609-639, (1960).
  • [4] Pavlov, B. S., “On the spectral theoy of non-self-adjoint differential operators”, Doklady Akademii Nauk: SSSR., 146: 1267-1270, (1962).
  • [5] Guseinov, G. S., “On the concept of spectral singularities”, Pramana Journal of Physics, 73(3): 587-603, (2009).
  • [6] Allahverdiev, B. P., Bairamov, E., Ugurlu, E., “Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions”, Journal of Mathematical Analysis and Applications, 401(1): 388-396, (2013).
  • [7] Bairamov, E., Aygar, Y., Eren B., “Scattering theory of impulsive Sturm-Liouville equations”, Filomat, 31(17): 5401-5409, (2017).
  • [8] Guseinov, G. S., “Boundary value problems for nonlinear impulsive Hamilton systems”, Journal of Computational and Applied Mathematics, 259: 780-789, (2014).
  • [9] Bairamov, E., Aygar Y., Oznur, G. B., “Scattering properties of eigenparameter-dependent impulsive Sturm-Liouville equations”, Bulletin of the Malaysian Mathematical Sciences Society, 43: 2769-2781, (2020).
  • [10] Mukhtarov, F. S., Aydemir, K., Mukhtarov, O.Sh., “Spectral analysis of one boundary value- transmission problem by means of Green’s function”, Electronic Journal of Mathematical Analysis and Applications, 2: 23-30, (2014).
  • [11] Milman, V. D., Myshkis, A. D., “On the stability of motion in the presence of impulses”, Siberian Mathematical Journal, 1: 233-237, (1960).
  • [12] 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).
  • [13] Perestyuk, N. A., Samoilenko, A. M., Stanzhitsii, A.N., “On the existence of periodic solutions of some classes of systems of differential equations with random impulse action”, Ukrainian Mathematical Journal, 53: 1061-1079, (2001).
  • [14] Samoilenka, A. M., Perestyuk, N. A., “Impulsive differential equations”, World Scientific, Singapore, (1995).
  • [15] Ugurlu, E., Bairamov, E., “Spectral analysis of eigenparameter dependent boundary value transmission problems”, Journal of Mathematical Analysis and Applications, 413(1): 482-494, (2014).
  • [16] Lakmeche, A., Arino, O., “Bifurcation of nontrivial periodic solutions of impulsive differential equations arising from chemotherapeutic treatment”, Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, 7: 265-287, (2000).
  • [17] Nenov, S. I., “Impulsive controllability and optimization problems in population dynamics”, Nonlinear Analysis, 36: 881-890, (1999).
  • [18] Kadakal, M., Mukhtarov, O.Sh., Mukhtarov, F. S., “Some spectral properties of Sturm-Liouville problem with transmission conditions”, Iranian Journal of Science and Technology Transaction A, Science , 29(2): 229-245, (2005).
  • [19] Marchenko, V. A., “Sturm-Liouville operators and applications”, Birkhauser, Verlag, (1986).
  • [20] Naimark, M. A., “Linear differential operators. Part II: Linear differential operators in Hilbert space”, World Scientific Publishing Co., Inc., River Edge, (1995).
APA BAYRAM E, Öznur G (2021). Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. , 1077 - 1087. 10.35378/gujs.796894
Chicago BAYRAM ELGIZ,Öznur Güler Başak Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. (2021): 1077 - 1087. 10.35378/gujs.796894
MLA BAYRAM ELGIZ,Öznur Güler Başak Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. , 2021, ss.1077 - 1087. 10.35378/gujs.796894
AMA BAYRAM E,Öznur G Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. . 2021; 1077 - 1087. 10.35378/gujs.796894
Vancouver BAYRAM E,Öznur G Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. . 2021; 1077 - 1087. 10.35378/gujs.796894
IEEE BAYRAM E,Öznur G "Scattering Function and The Resolvent of The Impulsive Boundary Value Problem." , ss.1077 - 1087, 2021. 10.35378/gujs.796894
ISNAD BAYRAM, ELGIZ - Öznur, Güler Başak. "Scattering Function and The Resolvent of The Impulsive Boundary Value Problem". (2021), 1077-1087. https://doi.org/10.35378/gujs.796894
APA BAYRAM E, Öznur G (2021). Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. Gazi University Journal of Science, 34(4), 1077 - 1087. 10.35378/gujs.796894
Chicago BAYRAM ELGIZ,Öznur Güler Başak Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. Gazi University Journal of Science 34, no.4 (2021): 1077 - 1087. 10.35378/gujs.796894
MLA BAYRAM ELGIZ,Öznur Güler Başak Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. Gazi University Journal of Science, vol.34, no.4, 2021, ss.1077 - 1087. 10.35378/gujs.796894
AMA BAYRAM E,Öznur G Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. Gazi University Journal of Science. 2021; 34(4): 1077 - 1087. 10.35378/gujs.796894
Vancouver BAYRAM E,Öznur G Scattering Function and The Resolvent of The Impulsive Boundary Value Problem. Gazi University Journal of Science. 2021; 34(4): 1077 - 1087. 10.35378/gujs.796894
IEEE BAYRAM E,Öznur G "Scattering Function and The Resolvent of The Impulsive Boundary Value Problem." Gazi University Journal of Science, 34, ss.1077 - 1087, 2021. 10.35378/gujs.796894
ISNAD BAYRAM, ELGIZ - Öznur, Güler Başak. "Scattering Function and The Resolvent of The Impulsive Boundary Value Problem". Gazi University Journal of Science 34/4 (2021), 1077-1087. https://doi.org/10.35378/gujs.796894
Sayfa Oluşturulma Tarihi
24-04-2024 4:30

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