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Öğe Inverse spectral problem for Dirac operator with discontinuous coefficient and polynomials in boundary condition(Taylor & Francis Ltd, 2016) Col, AynurIn this work, the inverse scattering problem for Dirac equations system with discontinuous coefficient and higher order polynomials of spectral parameter in the boundary condition is considered. The scattering function of the problem is defined, and its properties are investigated. The Marchenko-type main equation is obtained and it is shown that the potential is uniquely recovered by the scattering function. A generalization of Marchenko method is given for a class of Dirac operator.Öğe Inverse spectral problem for Sturm-Liouville operator with discontinuous coefficient and cubic polynomials of spectral parameter in boundary condition(Springer, 2015) Col, AynurIn this paper, the inverse scattering problem for the Sturm-Liouville operator with discontinuous coefficient and cubic polynomials of the spectral parameter in the boundary condition is considered. The scattering data of the problem is defined, and its properties are investigated. The modified Marchenko main equation is obtained and it is shown that the potential is uniquely recovered by the scattering data.Öğe Spectral Characteristics of the Sturm-Liouville Problem with Spectral Parameter-Dependent Boundary Conditions(2024) Col, AynurWe consider the Sturm-Liouville problem on the half line (0 ≤ x < ∞), where the boundary conditions contain polynomials of the spectral parameter. We define the scat- tering function and present the spectrum of the boundary value problem. The continuity of the scattering function is discussed. In a special case, the Levinson-type formula is intro- duced, demonstrating that the increment of the scattering function’s logarithm is related to the number of eigenvalues.Öğe Spectral properties for a system of Dirac equations with nonlinear dependence on the spectral parameter(De Gruyter Poland Sp Z O O, 2024) Col, AynurWe consider the boundary value problem generated by a system of Dirac equations with polynomials of spectral parameter in the boundary condition. We investigate the continuity of the scattering function and provide Levinson-type formula, which shows that the increment of the scattering function's logarithm is related to the number of eigenvalues of the boundary value problem.
