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Öğe Inverse scattering problem for Sturm-Liouville equation with a rational function of spectral parameter in boundary condition(Baku Engineering University, 2023) Çöl, AynurThe inverse scattering problem is analyzed for the Sturm-Liouville equation on the half line [0, ∞) with a rational function of spectral parameter in the boundary condition. The main equation is derived, its solvability is proved and it is presented that the potential is uniquely recovered in terms of the scattering data. © 2011 JCAM All rights reserved.Öğe On a scattering problem for Sturm-Liouville equation with a rational function of spectral parameter in boundary condition(Baku Engineering University, 2022) Çöl, AynurWe consider the Sturm-Liouville equation on the half line [0, ∞) with a rational function of spectral parameter in the boundary condition and investigate the corresponding scattering problem. Scattering data is obtained and its properties are examined. © 2011 JCAM All rights reserved.Öğe On an inverse problem for a class Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition(Applied Mathematical Sciences, 2010) Mamedov, Kh. R.; Çöl, AynurIn this paper, it is examined on the half line the inverse problem of scattering theory for a class Dirac operator with discontinuous coefficient and a spectral parameter in the boundary condition . The scattering function is defined as scattering data and its properties are investigated. It is obtained Gelfand-Levitan-Marchenko type main equation which plays an important role in the solution of inverse problem and it is shown the uniqueness of the solution of the inverse problem by using Fredholm alternative.Öğe On the expansion formula for a class of Dirac operator with discontinuous coefficient(International Journal of Computational Cognition, 2009) Mamedov, Kh. R.; Çöl, AynurIn this paper we consider a first order differential equation system with a discontinuous coefficient and spectral parameter dependent boundary condition in the half line. The operator interpretation of the given boundary value problem is investigated in the Hilbert space H = L2;½ ¡ 0;1;C2¢ £ C. The resolvent operator is constructed and the expansion formula with respect to eigenfunctions is obtainedÖğe On the inverse problem of the scattering theory for a class of systems of Dirac equations with discontinuous coefficient(European Journal of Pure Applied Mathematics, 2008) Mamedov, Kh. R.; Çöl, AynurIn this paper it is devoted to study the inverse scattering problem for a singular boundary value problem of generalized form of system Dirac type. The new representation for the solutions of the differential equations system is considered, the scattering function is defined and its properties are given. The main equation is obtained for the solution of the inverse problem and it is shown the uniqueness of the solution of the inverse problem of scattering theory on the half line
