On a Theorem of Bocher in the Theory of Ordinary Linear Differential Equations
Aurel Wintner · American Journal of Mathematics · 1954
for the n-rowed vector x. If there belongs to every constant vector c a solution vector x (t) of (1) satisfying x (t) -> c as t --oo (that is, if the initial condition x( oo ) can be assigned arbitrarily), then A (t) or (1) will be said to be of type (*) or to have (*) -character. It is clear from the principle of superposition (and from the existence of n linearly independent solution vectors) that, if A (t) is of type (*), then there belongs to every c exactly one x (t), and x( oo) lim x(t) must exist for every solution x(t). For the same reasons, A (t) is of type (*) if and only if there exists a (unique) fundamental matrix X (t) satisfying