27 citations · 101 across the 47 of their papers we have counts for
49 papers
Uniform stability of higher-order inverse spectral problems
Natalia P. Bondarenko
In this paper, the reconstruction of a linear differential operator of arbitrary order is studied by using two types of spectral characteristics: (i) eigenvalues and weig…
Third-order inverse spectral problem with the three-point boundary conditions
Natalia P. Bondarenko
In this paper, we study a new inverse spectral problem that consists in the recovery of the third-order differential equation from two spectra corresponding to the boundary conditi…
Uniform stability for the inverse Sturm-Liouville problem with eigenparameter-dependent boundary conditions
Natalia P. Bondarenko
We consider a class of self-adjoint Sturm-Liouville problems with rational functions of the spectral parameter in the boundary conditions. The uniform stability for direct and inve…
Inverse Sturm-Liouville problem with polynomials in the boundary condition and multiple eigenvalues
Egor E. Chitorkin, Natalia P. Bondarennko
In this paper, the inverse Sturm-Liouville problem with distribution potential and with polynomials of the spectral parameter in one of the boundary conditions is considered. We fo…
Local solvability and stability of an inverse spectral problem for higher-order differential operators
Natalia P. Bondarenko
In this paper, we for the first time prove local solvability and stability of an inverse spectral problem for higher-order () differential operators with distribution coeffi…
Local solvability and stability for the inverse Sturm-Liouville problem with polynomials in the boundary conditions
Egor E. Chitorkin, Natalia P. Bondarenko
In this paper, we for the first time prove local solvability and stability of the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the…
Regularization and inverse spectral problems for differential operators with distribution coefficients
Natalia P. Bondarenko
In this paper, we consider a class of matrix functions, which contains regularization matrices of Mirzoev and Shkalikov for differential operators with distribution coefficients of…
Inverse spectral problem for the Schrödinger operator on the square lattice
Dongjie Wu, Chuan-Fu Yang, Natalia Pavlovna Bondarenko
We consider an inverse spectral problem on a quantum graph associated with the square lattice. Assuming that the potentials on the edges are compactly supported and symmetric, we s…
Solving the inverse Sturm-Liouville problem with singular potential and with polynomials in the boundary conditions
Egor E. Chitorkin, Natalia P. Bondarenko
In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral p…
Solving Barcilon's inverse problems by the method of spectral mappings
Aiwei Guan, Chuanfu Yang, Natalia P. Bondarenko
In this paper, we consider Barcilon's inverse problem, which consists of the recovery of the fourth-order differential operator from three spectra. We obtain the relationship of Ba…
Inverse spectral problem for the third-order differential equation
Natalia P. Bondarenko
This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of t…
Spectral data asymptotics for the higher-order differential operators with distribution coefficients
Natalia P. Bondarenko
In this paper, the asymptotics of the spectral data (eigenvalues and weight numbers) are obtained for the higher-order differential operators with distribution coefficients and sep…
Reconstruction of higher-order differential operators by their spectral data
Natalia P. Bondarenko
This paper is concerned with inverse spectral problems for higher-order () ordinary differential operators. We develop an approach to the reconstruction from the spectral da…
Linear differential operators with distribution coefficients of various singularity orders
Natalia P. Bondarenko
In this paper, the linear differential expression of order with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for…
Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition
Natalia P. Bondarenko
In this paper, we develop two approaches to investigation of inverse spectral problems for a new class of nonlocal operators on metric graphs. The Laplace differential operator is…
A new approach to the inverse discrete transmission eigenvalue problem
Natalia P. Bondarenko, Vjacheslav A. Yurko
A discrete analog is considered for the inverse transmission eigenvalue problem, having applications in acoustics. We provide a well-posed inverse problem statement, develop a cons…
Finite-difference approximation of the inverse Sturm-Liouville problem with frozen argument
Natalia P. Bondarenko
This paper deals with the discrete system being the finite-difference approximation of the Sturm-Liouville problem with frozen argument. The inverse problem theory is developed for…
Inverse spectral problems for functional-differential operators with involution
Natalia P. Bondarenko
The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the se…
Solvability and stability of the inverse problem for the quadratic differential pencil
Natalia P. Bondarenko, Andrey V. Gaidel
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…
Local solvability and stability of the generalized inverse Robin-Regge problem with complex coefficients
Xiao-Chuan Xu, Natalia Pavlovna Bondarenko
We prove local solvability and stability of the inverse Robin-Regge problem in the general case, taking eigenvalue multiplicities into account. We develop the new approach based on…
Spectral data characterization for the Sturm-Liouville operator on the star-shaped graph
Natalia P. Bondarenko
The inverse spectral problems are studied for the Sturm-Liouville operator on the star-shaped graph and for the matrix Sturm-Liouville operator with the boundary condition in the g…
Inverse problem solution and spectral data characterization for the matrix Sturm-Liouville operator with singular potential
Natalia P. Bondarenko
The matrix Sturm-Liouville operator on a finite interval with singular potential of class and the general self-adjoint boundary conditions is studied. This operator gene…
Direct and inverse problems for the matrix Sturm-Liouville operator with the general self-adjoint boundary conditions
Natalia P. Bondarenko
The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class is…
Solving an inverse problem for the Sturm-Liouville operator with a singular potential by Yurko's method
Natalia P. Bondarenko
An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class is solved by the method of spectral mappings. We prove the uniquene…