About one characteristic of set of linear differential systems with non-negative coefficients

变系数矩微分方程线性系统的解

On the solutions to linear systems of moment differential equations with variable coefficients

针对解析系数的矩微分方程线性系统，本文研究解的存在性与解析性，并建立其与线性矩微分方程的关系，比较经典结果与一般矩微分情形。

Rough differential equations with path-dependent coefficients

We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives.

Connection coefficients and monodromy representations for a class of Okubo systems of ordinary differential equations, II

In this paper we construct explicit connection coefficients and monodromy representations for the canonical solution matrices of Okubo systems ${\rm II}^*$, ${\rm III}^*$, ${\rm IV}$ and ${\rm IV}^*$ of ordinary differential equations in Yokoyama's list. This work is a continuation of our previous work arXiv:1606.07187.

General Solution to Sequential Linear Conformable Fractional Differential Equations With Constant Coefficients

In this work, we give the general solution sequential linear conformable fractional differential equations in the case of constant coefficients for α(\in)(0,1]. In homogeneous case, we use a fractional exponential function which generalizes the corresponding ordinary function. In non-homogeneous case, we present to fractional the method of variation of parameters for a particular solution of sequential linear conformable fractional differential equations.

Hyers-Ulam stability for differential systems with $2\times 2$ constant coefficient matrix

We explore the Hyers-Ulam stability of perturbations for a homogeneous linear differential system with $2\times 2$ constant coefficient matrix. New necessary and sufficient conditions for the linear system to be Hyers-Ulam stable are proven, and for the first time, the best (minimal) Hyers-Ulam constant for systems is found in some cases. Several examples are provided. Obtaining the best Hyers-Ulam constant for second-order constant coefficient differential equations illustrates the applicability of the strong results.

Power series with Taylor coefficients of sum-product type and algebraic differential equations /SP-series and the interplay between their resurgence and differential properties

The article is based on the differential properties of the inner generators (singularities) that occur while handling SP series (sum product series), power series whose Taylor coefficients can be written as sum-product combinations. It is an elaboration with numerical details and some explicit calculations of the chapter 6 of the joint article with Ecalle on these series. For all polynomial inputs $f$ and all monomial inputs $F$, the inner generators corresponding to them verify ordinary differential equations of linear homogeneous type with polynomial coefficients. Numerical results strongly …

Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices

A method of generating differential operators is used to solve the spectral problem for a generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential operator with polynomial coefficients of the first order that has a finite sequence of polynomial eigenfunctions generalising the operator considered by M. Kac. In addition, we explain spectral properties of two related tridiagonal matrices whose shape differ from our generalisation.

On the spectrum of second order differential operators with complex coefficients

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 maximal-accretive realisations of the differential expression.

Explicit Representations of Green's Function for Linear Fractional Differential Operator with Variable Coefficients

We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0, \infty)$. Using the explicit representations for Green's function, we obtain explicit representations for solution of inhomogeneous fractional differential equation with variable coefficients of general type. Therefore the method of Green's function, which was developed in previous research for solution of fractional differential equation with constant coeff…

具有多项式系数的秩2交换微分算子

Commuting differential operators of rank 2 with polynomial coefficients

该研究考察多项式系数的自伴交换常微分算子及其在第一Weyl代数中形成的交换子代数，并给出秩2交换算子的新例子。

Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class

A limiting property of the nearest-neighbor recurrence coefficients for multiple orthogonal polynomials from a Nevai class is investigated. Namely, assuming that the nearest-neighbor coefficients have a limit along rays of the lattice, we describe it in terms of the solution of a system of partial differential equations. In the case of two orthogonality measures the differential equation becomes ordinary. For Angelesco systems, the result is illustrated numerically.

Differential transcendency in the theory of linear differential systems with constant coefficients

In this paper we consider a reduction of a non-homogeneous linear system of first order operator equations to a totally reduced system. Obtained results are applied to Cauchy problem for linear differential systems with constant coefficients and to the question of differential transcendency.