On the solvability of boundary value problems for linear differential-algebraic equations with constant coefficients

TL;DR

This paper investigates the conditions under which boundary value problems for linear differential-algebraic equations with constant coefficients are uniquely solvable, using canonical forms and parameterization methods.

Contribution

It introduces a criterion for unique solvability of such boundary value problems based on the Weierstrass canonical form and parameterization approach.

Findings

Derived a solvability criterion using Weierstrass canonical form

Applied parameterization to boundary value problems

Established conditions for unique solutions

Abstract

We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of the solution at the left endpoint of the interval. Applying the Weierstrass canonical form to the matrix pair associated with the differential-algebraic equation, we obtain a criterion for the unique solvability of the problem.