Related papers: Recovering Differential Operators on Spatial Netwo…
This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…
The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the…
This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…
We suggest a new concept of functional-differential operators with constant delay on geometrical graphs that involves {\it global} delay parameter. Differential operators on graphs model various processes in many areas of science and…
First order integro-differential operators on a finite interval are studied. Properties of spectral characteristic are established, and the uniqueness theorem is proved for the inverse problem of recovering operators from their spectral…
In this paper we study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from two spectra. We give a reconstruction algorithm and establish existence and uniqueness of reconstruction. Our approach…
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…
Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.
Inverse problems for differential pencils with nonlocal conditions are investigated. Several uniqueness theorems of inverse problems from the Weyl-type function and spectra are proved, which are generalizations of the well-known Weyl…
The author studies the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this star-like graph centered at the origin as its vertex, there are attached $m$ edges that imposed the Sturm-Liouville operator with…
We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…
In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded…
In this study, we investigate the traces and solutions of inverse nodal problems of discontinuous Sturm-Liouville operators with retarded argument and with a finite number of transmission conditions.
Recently, there appeared a significant interest in inverse spectral problems for non-local operators arising in numerous applications. In the present work, we consider the operator with frozen argument $ly = -y''(x) + p(x)y(x) + q(x)y(a),$…
We solve the inverse spectral problem of recovering the singular potentials $q\in W^{-1}_{2}(0,1)$ of Sturm-Liouville operators by two spectra. The reconstruction algorithm is presented and necessary and sufficient conditions on two…
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…
In this paper inverse problems for Dirac operator with nonlocal conditions are considered. Uniqueness theorems of inverse problems from the Weyl-type function and spectra are provided, which are generalizations of the well-known Weyl…
A new method for solving inverse spectral problems on quantum star graphs is proposed. The method is based on Neumann series of Bessel functions representations for solutions of Sturm-Liouville equations. The representations admit estimates…
This paper deals with the inverse spectral problem for a non-self-adjoint Sturm-Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential $q$ is known a priori on a subinterval $ \left[ b,\pi…
We consider an inverse spectral problem that consists in the recovery of the differential expression coefficients for higher-order operators with separated boundary conditions from the spectral data (eigenvalues and weight numbers). This…