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

Disconjugacy of a second order linear differential equation and periodic solutions