A Differential-Algebraic Boundary Value Constant-Delay Problem in the Case of a Variable-Rank Matrix at the Derivative

The question of finding the solvability conditions of a boundary value problem and its solutions is studied for a linear differential-algebraic constant-delay system in the case of a variable-rank matrix at the derivative. The objective formulated in this paper is to continue the studies on the solubility conditions of linear Noetherian boundary value problems for the systems of functional differential equations given in the monographs of Myshkis, Azbelev, Maksimov, Rakhmantullina, Samoilenko, and Boichuk, when the Moore–Penrose matrix pseudoinverse technique is essentially engaged. The solvability conditions and solution of a Noetherian boundary value problem have been found for a differential algebraic constant-delay system. The proposed solvability conditions and solution of the boundary value problem with a linear differential-algebraic constant-delay system in the case of a variable-rank matrix at the derivative are illustrated with the use of detailed examples.