GENERAL SOLUTIONS OF LINEAR MATRIX CANONICAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS

摘要

Let us consider the following linear homogeneous matrix first-order differential equation:rn(p - A)X = 0, where A=A(t), t∈I, is a continuous (n × n)-matrix function and p is the differentiation operator in t. It is known that the solution X(t) of this equation satisfying the initial condition X(t_0) = E, where E is the identity (n × n)-matrix and t_0 is an arbitrary fixed point of an interval I, can be represented in the form of the seriesrn E + ∫_(to)~t Adt+ ∫_(to)~t Adt ∫_(to)~t Adt + …,rnwhich absolutely and uniformly converges on any closed interval on which the matrix function A is continuous.