Disconjugacy of a second order linear differential equation and periodic solutions

Abstract

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.