This paper is concerned with
the system of differential equations
(1)
where A(t) is an n×n matrix of locally integrable complexvalued functions on [0,ω)
and x(t) is an n-dimensional column vector. The class of matrices A(t) such that (1)
has a nontrivial solution x0(t) satisfying limt→ω|x0(t)| = 0 is denoted by
Ω0; the class of matrices A(t) such that (1) has a solution x∞(t) satisfying
limt→ω|x∞(t)| = +∞ is denoted by Ω∞. If P is a projection then ΩP0 denotes the
class of matrices A(t) such that (1) has a nontrivial solution x0(t) satisfying
limt→ω|Px0(t)| = 0. Sufficient conditions are given for A(t) ∈ Ω0,A(t) ∈ Ω∞ and
A(t) ∈ ΩP0; the result, obtained include as special cases theorems of Coppel,
Hartman, and Milloux.
