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This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

Spectral Theory · Mathematics 2024-09-05 E. E. Chitorkin , N. P. Bondarenko

The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…

Classical Analysis and ODEs · Mathematics 2008-04-15 R. F. Efendiev

We consider a quadratic matrix boundary value problem with equations and boundary conditions dependent on a spectral parameter. We study an inverse problem that consists in recovering the differential pencil by the so-called Weyl matrix. We…

Spectral Theory · Mathematics 2013-01-15 Natalia Bondarenko

The inverse spectral problem for the second-order differential pencil with quadratic dependence on the spectral parameter is studied. We obtain sufficient conditions for the global solvability of the inverse problem, prove its local…

Spectral Theory · Mathematics 2021-03-18 Natalia P. Bondarenko , Andrey V. Gaidel

In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their…

Spectral Theory · Mathematics 2020-08-10 Maria Kuznetsova

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants.…

Spectral Theory · Mathematics 2007-05-23 R. O. Hryniv , Ya. V. Mykytyuk

The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…

Spectral Theory · Mathematics 2021-09-01 Natalia Bondarenko

We consider a pencil of non-self-adjoint matrix Sturm-Liouville operators on the half line and study the inverse problem of constructing this pencil by its Weyl matrix. A uniqueness theorem is proved, and a constructive algorithm for the…

Spectral Theory · Mathematics 2013-02-12 Natalia Bondarenko , Gerhard Freiling

The stated paper is dedicated to one of the inverse problems of spectral theory. It is necessary to define matrix (constant) coefficients of some quadratic pencil, if the eigenvalues of this pencil are known. Furthermore, it is known that…

Spectral Theory · Mathematics 2015-12-02 N. A. Aliyev , Y. Y. Mustafayeva , R. F. Efendiyev

Inverse spectral problems consist in recovering operators by their spectral characteristics. The problem of recovering the Sturm-Liouville operator with one frozen argument was studied earlier in works of various authors. In this paper, we…

Spectral Theory · Mathematics 2025-04-14 Maria Kuznetsova

The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…

Spectral Theory · Mathematics 2020-08-18 Sergey Buterin

Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…

Spectral Theory · Mathematics 2019-11-25 Natalia Bondarenko , Vjacheslav Yurko

We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…

Spectral Theory · Mathematics 2014-01-14 Natalia Bondarenko

We study Sturm-Liouville operators on closed sets of a special structure, which are sometimes referred as time scales and often appear in modelling various real processes. Depending on the set structure, such operators unify both…

Spectral Theory · Mathematics 2021-07-13 S. A. Buterin , M. A. Kuznetsova , V. A. Yurko

In recent years, there appeared a considerable interest in the inverse spectral theory for functional-differential operators with constant delay. In particular, it is well known that, for each fixed $\nu\in\{0,1\},$ the spectra of two…

Spectral Theory · Mathematics 2021-02-17 Nebojša Djurić , Sergey Buterin

This research was devoted to investigate the inverse spectral problem of Sturm-Liouville operator with many frozen arguments. Under some assumptions, the authors obtained uniqueness theorems. At the end, a numerical simulation for the…

Spectral Theory · Mathematics 2024-07-23 Chung-Tsun Shieh , Tzong-Mo Tsai

In this paper, a Sturm-Liouville boundary value problem equiped with conformable fractional derivates is considered. We give some uniqueness theorems for the solutions of inverse problems according to the Weyl function, two given spectra…

Classical Analysis and ODEs · Mathematics 2022-03-23 A. Sinan Ozkan , İbrahim Adalar

We consider second order linear differential operators possessing a term depending on the unknown function with a fixed argument and study the uniqueness of recovering the operators from the spectrum. We also obtain a constructive procedure…

Spectral Theory · Mathematics 2020-01-28 N. P. Bondarenko , S. A. Buterin , S. V. Vasiliev

The matrix Sturm-Liouville operator on a finite interval with singular potential of class $W_2^{-1}$ and the general self-adjoint boundary conditions is studied. This operator generalizes the Sturm-Liouville operators on geometrical graphs.…

Spectral Theory · Mathematics 2020-07-16 Natalia P. Bondarenko

We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori…

Numerical Analysis · Mathematics 2009-09-29 Norbert Roehrl