Araştırma Makalesi
Yıl 2021,
Cilt: 34 Sayı: 4, 1077 - 1087, 01.12.2021
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 Kelimeler
Boundary value problem Density function Impulsive condition Resolvent operator Spectral parameter
Kaynakça
- 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).
- 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).
- Referans5: Guseinov, G.S., “On the concept of spectral singularities”, Pramana, J. Phys., 73(3):587-603, (2009).
- 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).
- Referans7:Bairamov, E., Aygar, Y., Eren B., “Scattering theory of impulsive Sturm-Liouville equations”, Filomat, 31(17):5401-5409, (2017).
- Referans8: Guseinov, G.S., “Boundary value problems for nonlinear impulsive Hamilton systems”, J. Comput. Appl. Math., 259:780-789, (2014).
- 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).
- 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).
- 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).
- 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).
- 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).
Yıl 2021,
Cilt: 34 Sayı: 4, 1077 - 1087, 01.12.2021
Öz
Kaynakça
- 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).
- 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).
- Referans5: Guseinov, G.S., “On the concept of spectral singularities”, Pramana, J. Phys., 73(3):587-603, (2009).
- 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).
- Referans7:Bairamov, E., Aygar, Y., Eren B., “Scattering theory of impulsive Sturm-Liouville equations”, Filomat, 31(17):5401-5409, (2017).
- Referans8: Guseinov, G.S., “Boundary value problems for nonlinear impulsive Hamilton systems”, J. Comput. Appl. Math., 259:780-789, (2014).
- 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).
- 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).
- 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).
- 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).
- 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).
Toplam 11 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Mathematics |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Aralık 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 34 Sayı: 4 |