Related papers: Inverse spectral problem for a third-order differe…
The direct and inverse problems for a third-order self-adjoint differential operator with non-local potential functions are considered. Firstly, the multiplicity for eigenvalues of the operator is analyzed, and it is proved that the…
Inverse spectral problem for a self-adjoint differential operator, which is the sum of the operator of the third derivative on a finite interval and of the operator of multiplication by a real function (potential), is solved. Closed system…
Sum of a second derivative operator with periodic boundary conditions and an integral operator of rank one (non-local potential) is studied in this manuscript. Not only spectral analysis is conducted for this operator but the inverse…
Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…
The inverse problem for the differential operator pencil with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator…
A third order self-adjoint differential operator with periodic boundary conditions and an one-dimensional perturbation has been considered. For this operator, we first show that the spectrum consists of simple eigenvalues and finitely many…
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 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…
Direct and inverse scattering problems for a third-order self-adjoint differential operator on the whole axis are studied. This operator is the sum of three summands: operator of third derivative, operator of multiplication by a function,…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
For a Dirac operator with non-local potential on a finite segment, a method of reconstruction of non-local potential from the spectral data is developed. Description of spectral data for such class of operators is given.
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 the differential expression coefficients from the spectral…
Direct and inverse scattering problem for an operator with non-local potential is solved in the paper. The method is based on the Riemann boundary value problem on a bundle of three straight lines. Description of scattering problem data is…
The paper considers the general form of self-adjoint boundary value problems for momentum operators with nonlocal potentials. We give an analysis of the eigenvalue distribution as zeros of the characteristic functions, for which their…
Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an…
Inverse scattering problem for an operator, which is a sum of the operator of the third derivative and of an operator of multiplication by a real function, is solved. The main closed system of equations of inverse problem is obtained. This…
Inverse spectral problems for Sturm-Liouville operators on a finite interval with non-separated boundary conditions are studied in the central symmetric case, when the potential is symmetric with respect to the middle of the interval. We…
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…
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 considered on a star-shaped graph with nonlocal integral…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…