On linear equations with polynomial coefficients

On Global Non-oscillation of Linear Ordinary Differential Equations with Polynomial Coefficients

Based on a new explicit upper bound for the number of zeros of exponential polynomials in a horizontal strip, we obtain a uniform upper bound for the number of zeros of solutions to an ordinary differential equation near its Fuchsian singular point, provided that any two distinct characteristic exponents at this point have distinct real parts. The latter result implies that a Fuchsian different...

Exact linear modeling with polynomial coefficients

Given a finite set of polynomial, multivariate, and vector-valued functions, we show that their span can be written as the solution set of a linear system of partial differential equations (PDE) with polynomial coefficients. We present two different but equivalent ways to construct a PDE system whose solution set is precisely the span of the given trajectories. One is based on commutative algeb...

Linear Differential Algebraic Equations with Constant Coefficients

Differential-algebraic equations (DAEs) arise in a variety of applications. Their analysis and numerical treatment, therefore, plays an important role in modern mathematics. The paper gives an introduction to the topics of DAEs. Examples of DAEs are considered showing their importance for practical problems. Some essential concepts that are really essential for understanding the DAE systems are...

Linear Transport Equations with mu-Monotone Coefficients

Linear fractional differential equations with variable coefficients

This work is devoted to the study of solutions around an α-singular point x0 ∈ [a, b] for linear fractional differential equations of the form [Lnα(y)](x) = g(x, α), where [Lnα(y)](x) = y(nα)(x)+ n−1 ∑ k=0 ak(x)y (kα)(x) with α ∈ (0, 1]. Here n ∈ N , the real functions g(x) and ak(x) (k = 0, 1, . . . , n−1) are defined on the interval [a, b], and y(nα)(x) represents sequential fractional deriva...