On singular points of linear differential equations with real coefficients

A Uniqueness Result on Ordinary Differential Equations with Singular Coefficients

We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the order of singularities of the coefficients and provide examples to illustrate the results. 1. Results and examples Classical results on the existence and uniqueness of ordinary differential equations are mostly concerned with continuous coeffici...

On Singular Solutions of Linear Functional Differential Equations with Negative Coefficients

On Singular Points of Quasilinear Differential and Differential-algebraic Equations

We show how certain singularities of quasilinear diierential and diierential-algberaic equations can be resolved by taking the solutions to be integral manifolds of certain distributions rather than curves with speciic parametrization.

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 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...