Related papers: On classification of singular matrix difference eq…
We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the…
Concatenating matrices is a common technique for uncovering shared structures in data through singular value decomposition (SVD) and low-rank approximations. The fundamental question arises: How does the singular value spectrum of the…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…
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…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$…
A Dirichlet-type problem is studied for an equation of even order with variable coefficients. A criterion for the uniqueness of a solution is given. The solution is built in the form of a Fourier series. When justifying the convergence of…
In this article, we study the singular case of an homogeneous generalized discrete time system with given initial conditions. We consider the matrix pencil singular and provide necessary and sufficient conditions for existence and…
The main objective of this talk is to develop a matrix pencil approach for the study of an initial value problem of a class of singular linear matrix differential equations whose coefficients are constant matrices. By using matrix pencil…
Matrix perturbation inequalities, such as Weyl's theorem (concerning the singular values) and the Davis-Kahan theorem (concerning the singular vectors), play essential roles in quantitative science; in particular, these bounds have found…
Isolated hypersurface singularities come equipped with distinguished bases of their Milnor lattices and with upper triangular integral matrices, which are called here distinguished matrices. These matrices form an orbit of a braid group and…
In this paper, we prove that there exists a unique weak solution to the mixed boundary value problem for a general class of semilinear second order elliptic partial differential equations with singular coefficients. Our approach is…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
We develop the basic theory of matrix-valued Weyl-Titchmarsh M-functions and the associated Green's matrices for whole-line and half-line self-adjoint Hamiltonian finite difference systems with separated boundary conditions.
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. Well-posedness of differential equation problems thus involves…
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a…
In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon. We show that usual central finite differences, which are second…
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…