is disconjugate on [a,b] if and only if there exists a solution which is positive on [a,b],
in the case that A(t) is scalar-valued. In this note we generalize this simple
result to the case where A(t) = (aij(t)) is an n × n matrix-valued function
which satisfies certain generalized sign conditions. These results apply, for
instance, if the off diagonal elements are nonnegative. Simple necessary and
sufficient conditions are given for disconjugacy if A(t) ≡ A and these are used to
construct examples showing the necessity of sign conditions on A(t) for the
above mentioned results and other results of Sturm type for systems to be
valid.
