A converse of Sturm's separation theorem

We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a turning point in the principal part of the equation. Related results are discu...

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Veröffentlicht in:	Electronic journal of qualitative theory of differential equations 2021-01, Vol.2021 (78), p.1-8
Hauptverfasser:	Gholizadeh, Leila, Mingarelli, Angelo
Format:	Artikel
Sprache:	eng
Schlagworte:	indefinite leading term indefinite principal part recurrence relations sturm separation property sturm separation theorem
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Beschreibung
Zusammenfassung:	We show that Sturm's classical separation theorem on the interlacing of the zeros of linearly independent solutions of real second order two-term ordinary differential equations necessarily fails in the presence of a turning point in the principal part of the equation. Related results are discussed.
ISSN:	1417-3875 1417-3875
DOI:	10.14232/ejqtde.2021.1.78