On the structure of the general solution and conditions of solvability of the Cauchy problem for degenerate linear systems of higher-order differential equations

Abstract

For a system of linear differential equations of order $p$ with identically degenerate coefficient matrix of the leading derivatives, we establish conditions under which it has a general solution of the Cauchy type. The structure of this solution is determined. Conditions for the existence and uniqueness of a solution of the corresponding initial-value problem are also found.