  The present paper is devoted to a new criterion for disconjugacy of a second
order linear differential equation. Unlike most of the classical sufficient
conditions for disconjugacy, our criterion does not involve assumptions on the
smallness of the coefficients of the equation. We compare our criterion with
several known criteria for disconjugacy, for which we provide detailed proofs,
and discuss the applications of the property of disconjugacy to the problem of
factorization of linear ordinary differential operators, and to the proof of
the generalized Rolle's theorem. The paper is self-contained, and may serve as
a brief introduction to theory of disconjugacy of a second order linear
differential equation.
