A converse of Sturm's separation theorem | Zendy

Leila Gholizadeh | Zendy; Angelo B. Mingarelli | Zendy

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A converse of Sturm's separation theorem

Author(s) -

Leila Gholizadeh,

Angelo B. Mingarelli

Publication year - 2021

Publication title -

electronic journal of 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.

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