Related papers: Inverse nodal problems for Dirac-type integro-diff…

The operator associated to the angular part of the Dirac equation in the Kerr-Newman background metric is a block operator matrix with bounded diagonal and unbounded off-diagonal entries. The aim of this paper is to establish a variational…

We consider, in a Hilbert space $H$, the convolution integro-differential equation $u''(t)-h*Au(t)=f(t)$, $0\le t\le T$, $h*v(t)=\int_0^t h(t-s)v(s) ds$, where $A$ is a linear closed densely defined (possibly selfadjoint and/or positive…

In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…

The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in…

In this paper, we investigate existence and uniqueness of solutions of nonlinear Volterra-Fredholm impulsive integrodifferential equations. Utilizing theory of Picard operators we examine data dependence of solutions on initial conditions…

We study an inverse problem for variable coefficient fractional parabolic operators of the form $(\partial_t -\operatorname{div}(A(x) \nabla_x)^s + q(x,t)$ for $s\in(0,1)$ and show the unique recovery of $q$ from exterior measured data.…

We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian-Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given…

In this paper the complete spectral analysis of the operators is carried out and also with help of generalized normalizing numbers the inverse problem is solved.

Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving boundary value problems for…

We consider the linearized electrical impedance tomography problem in two dimensions on the unit disk. By a linearization around constant coefficients and using a trigonometric basis, we calculate the linearized Dirichlet-to-Neumann…

This paper deals with inverse problems subject to imprecise or vague information of some involved data by means of interval-valued functions. To provide interval solutions to the inverse problems we have adopted a perturbed collage-based…

We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…

For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.

Our work concerns the study of inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations. We recover nonlinear terms in the semilinear equations from the knowledge of…

This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish…

In this paper, we investigate the inverse generator problem for abstract degenerate Volterra integro-differential equations in locally convex spaces. The classes of degenerate $(a,k)$-regularized $C$-resolvent families and degenerate mild…

We consider the inverse problem for the dynamical system with discrete Schr\"odinger operator and discrete time. As an inverse data we take a \emph{response operator}, the natural analog of the dynamical Dirichlet-to-Neumann map. We derive…

The differential operators pencil recovery uniqueness theorem is proved in our article. Novelty of this result is not equation coefficient recovery, but boundary conditions coefficients recovery. We show that all conditions of the theorem…

This paper is concerned with an inverse source problem for the stochastic biharmonic operator wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical…

We study general conditions under which the computations of the index of a perturbed Dirac operator $D_{s}=D+sZ$ localize to the singular set of the bundle endomorphism $Z$ in the semi-classical limit $s\to \infty $. We show how to use…