2010/05/31 by V. Ya. Derr, Derr, V. Ya., V.Ya. Derr
Computer Science · Mathematics · Physics and Astronomy · #34B05 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations #Quantum chaos and dynamical systems #math.CA #msc:34B05
paper · pdf · doi:10.48550/arxiv.1005.5646
arxiv created 2010/05/31 · openalex publication_date 2010/05/31 · arxiv updated 2010/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.