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arXiv · 2109.06953

The converse of Sturm's Separation Theorem

L. Gholizadeh·A. B. Mingarelli
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Abstract

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 unique turning point in the principal part of the equation. Related results are discussed. The last section contains an extension of the main result to a finite number of turning points.

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L. Gholizadeh, A. B. Mingarelli. 2021-09-14. The converse of Sturm's Separation Theorem. https://arxiv.org/abs/2109.06953

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