Related papers: On classification of singular matrix difference eq…
This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed data: \begin{cases} -\operatorname{div}(A(x,D u))=g-\operatorname{div} f…
We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…
The quasi-variational inequalities play a significant role in analyzing a wide range of real-world problems. However, these problems are more complicated to solve than variational inequalities as the constraint set is based on the current…
In this work we consider the primal mixed variational formulation of the Poisson equation with a line source. The analysis and approximation of this problem is non-standard as the line source causes the solutions to be singular. We start by…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…
Under certain conditions, we give an estimate from above on the number of differential equations of order $r+1$ with prescribed regular singular points, prescribed exponents at singular points, and having a quasi-polynomial flag of…
We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be…
The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…
The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…
We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…
We discuss existence, non-uniqueness and regularity of one- and two-sided solutions of initial value problems for scalar quasi-linear ordinary differential equations where the initial condition corresponds to an impasse point of the…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
The Weyl-Sims classification for a second-order ordinary differential equation with general complex coefficients is investigated. Connections are then established between the associated m-function and the spectral properties of…
We consider a variational problem with boundary singularity and Dirichlet condition. We give a blow-up analysis for sequences of solutions of an equation with exponential nonlinearity. Also, we derive a compactness criterion under some…
We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous…
We study the local classification of higher order Fuchsian linear differential equations under various refinements of the classical notion of the "type of differential equation" introduced by Frobenius. The main source of difficulties is…