Open AccessA converse of Sturm's separation theorem
Author(s) -
Leila Gholizadeh,
Angelo B. Mingarelli
Publication year - 2021
Publication title -
electronic journal on the qualitative theory of differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.524
H-Index - 33
ISSN - 1417-3875
DOI - 10.14232/ejqtde.2021.1.78
Subject(s) - mathematics , converse , ordinary differential equation , order (exchange) , interlacing , sturm–liouville theory , separation (statistics) , mathematical analysis , differential equation , pure mathematics , statistics , boundary value problem , geometry , finance , computer science , economics , operating system
We show that Sturm's classical separation theorem on the interlacingof the zeros of linearly independent solutions of real second ordertwo-term ordinary differential equations necessarily fails in the presenceof a turning point in the principal part of the equation. Related resultsare discussed.