In this study, transformation operator, some properties of kernel, properties of spectral characteristics and also uniquiness theorems for the inverse problems are studied for a class of Sturm-Liouville differential operators which have discontinuity conditions inside a finite interval. 2005 Elsevier Inc. All rights reserved.
In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.
In this paper, we consider the inverse spectral problem for the impulsive Sturm-Liouville differential pencils on [0, π] with the Robin boundary conditions and the jump conditions at the point 2. We prove that two potentials functions on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potentials given on where is the spectral parameter, p(x) ∈ W 1 2 [0, ], q(x) ∈ L 2 [0, ] are real-valued functions, is a real number, and > 0, ≠ 1. Here we denote by W m 2 [0, ] the space of functions f (x), x ∈ [0, ], such
We investigate a problem for the Dirac differential operators in the case where an eigenparameter not only appears in the differential equation but is also linearly contained in a boundary condition. We prove uniqueness theorems for the inverse spectral problem with known collection of eigenvalues and normalizing constants or two spectra.
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