Half-Inverse Problem For Dirac Operator With Boundary And Transmission Conditions Dependent Spectral Parameter Polynomially

Yıl 2019, Cilt: 40 Sayı: 4, 902 - 908, 31.12.2019

Yalçin Güldü Merve Arslantaş

https://doi.org/10.17776/csj.637861

Öz

 In this paper, half-inverse problem is considered
for Dirac equations with boundary and finite number of transmission conditions
depending polynomially on the spectral parameter, if the potential is given
over the half of the considered interval and if one spectrum is known then,
potential function  on the whole
interval and the other coefficients of the considered problem can be determined
uniquely.

Anahtar Kelimeler

Dirac equations, transmission conditions, spectral parameter

Destekleyen Kurum

CÜBAP

Proje Numarası

F-543

Kaynakça

• [1] Hochstadt, H., Lieberman, B., An inverse Surm-Liouville Problem with mixed given data, Siam J. Appl. Math., 34 -4 (1978) 676-680.
• [2] Hald, O. H., Discontiuous inverse eigenvalue problems, Comm. Pure Appl. Math., 37 (1984) 539-577.
• [3] Buterin, S., On half inverse problem for differential pencils with the spectral parameter in boundary conditions, Tamkang J. Math. , 42 (2011) 355-364.
• [4] Özkan, A. S., Half inverse problem for a class of differential operator with eigenvalue dependent boundary and jump conditions, Journal of Advanced Research in Applied Mathematics, 4 (2011) 43-49.
• [5] Özkan, A. S., Half-inverse Sturm-Liouville problem with boundary and discontinuity conditions dependent on the spectral parameter, Inverse Problems in Science and Engineering. 22-5 (2013) 848-859.
• [6] Sakhnovich, L., Half inverse problems on the finite interval, Inverse Probl., 17 (2001) 527-532.
• [7] Wang, YP., Inverse problems for Sturm-Liouville operators with interior discontinuities and boundary conditions dependent on the spectral parameter, Math. Methods Appl. Sci., 36 (2013) 857-868.
• [8] Yang, C-Fu., Uniqueness theorems for differential pencils with eigenparameter boundary conditions and transmission conditions, 255 (2013) 2615-2635.
• [9] Yang, C-Fu., Inverse problems for Dirac equations polynomially depending on the spectral parameter, Applicable Analysis, (2015).
• [10] Yang, C-Fu. (2011). Hochstadt-Lieberman theorem for Dirac operator with eigenparameter dependent boundary conditions, Nonlinear Anal. Ser. A: Theory Methods Appl., 74 (2011) 2475-2484.
• [11] Yang, C-Fu., Determination of Dirac operator with eigenparameter dependent boundary conditions from interior spectral data, Inv. Probl. Sci. Eng., 20 (2012) 351-369.
• [12] Yang, C-Fu, Huang Z-You., A half-inverse problem with eigenparameter dependent boundary conditions, Numer. Func. Anal. Opt. , 31 (2010) 754-762.
• [13] Walter, J., Regular eigenvalue problems with eigenvalue parameter in the boundary conditions, Math Z., 133 (1973) 301-312.
• [14] Fulton, C. T. (1977). Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. R. Soc. Edinburgh, A77 (1977) 293-308.
• [15] Amirov, R. Kh.; Keskin, B.; Özkan, A. S., Direct and inverse problems for the Dirac operator with spectral parameter linearly contained in boundary condition., Ukrainian Math. J., 61-9 (2009) 1365-1379.
• [16] Binding, P. A.; Browne, P. J.; Watson, B. A., Inverse spectral problems for Sturm--Liouville equations with eigenparameter dependent boundary conditions, J. London Math. Soc. 62 (2000) 161--182.
• [17] Binding, P. A.; Browne, P. J.; Watson, B. A., Equivalence of inverse Sturm--Liouville problems with boundary conditions rationally dependent on the eigenparameter, J. Math. Anal. Appl. 291 (2004) 246-261.
• [18] Binding, P. A.; Browne, P. J.; Seddighi, Sturm-Liouville problems with eigenparameter dependent boundary conditions, Proc. Edinb. Math. Soc. 37-2 (1993) 57-72.
• [19] Browne, P. J.; Sleeman, B. D., A uniqueness theorem for inverse eigenparameter dependent Sturm-Liouville problems, Inverse Problem, 13 (1997) 1453-1462.
• [20] Chernozhukova, A.; Freiling, G., A uniqueness theorem for the boundary value problems with non- linear dependence on the spectral parameter in the boundary conditions, Inverse Problems in Science and Engineering, 17-6 (2009) 777-785.
• [21] Freiling, G.; Yurko, V. A., Inverse problems for Sturm-Liouville equations with boundary conditions polynomially dependent on the spectral parameter. Inverse Problems 26-5 (2010) 17.
• [22] Gasymov, M. G.; Levitan, B. M., The Inverse Problem for the Dirac System, Dokl. Akad. Nauk SSR, 167 (1966) 967-970.
• [23] Gasymov, M. G., The inverse scattering problem for a system of Dirac equations of order 2n. Dokl. Akad. Nauk SSSR 169 (1966) 1037-1040 (Russian); 11 676-678.
• [24] Gasymov, M. G.; Dzhabiev, T. T., On the Determination of the Dirac System from Two Spectra, Transactions of the Summer School on Spectral Theory Operator, Baku/ELM., (1975) 46-71.
• [25] Guliyev, N. J., Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions. Inverse Problems 21-4 (2005) 1315-1330.
• [26] Guseinov, IM., On the representation of Jost solutions of a system of Dirac differential equations with discontinuous coefficients, Izv. Akad. Nauk Azerb. SSR., 5 (1999) 41-45.
• [27] Güldü, Y., On discontinuous Dirac operator with eigenparameter dependent boundary and two transmission conditions. Bound. Value Probl., (2016) 135- 19.
• [28] Keskin, B., Inverse spectral problems for impulsive Dirac operators with spectral parameters contained in the boundary and discontinuity conditions polynomially, Neural Comput&Applic. ,23 (2013) 1329-1333.
• [29] Keskin, B., Inverse problems for impulsive Dirac operators with spectral parameters contained in the boundary and multitransfer conditions, Math. Methods in Applied Sciences, (2013) 38.
• [30] Mennicken, R.; Schmid, H., Shkalikov, A. A., On the eigenvalue accumulation of Sturm-Liouville problems depending nonlinearly on the spectral parameter, Math. Nachr., 189 (1998) 157-170.
• [31] Schmid, H.; Tretter, C., Singular Dirac systems and Sturm-Liouville problems nonlinear in the spectral parameter, J. Differ. Eqns., 181-2 (2002) 511-542.
• [32] Yurko, V. A., Boundary value problems with a parameter in the boundary conditions, Izv. Akad. Nauk Armyan. SSR, Ser. Mat., 19-5 (1984) 398-409.
• [33] Yurko, V. A. (2000). An inverse problem for pencils of differential operators, Mat Sbornik, 191-10 (2000) 137-158.