The converse of Sturm's Separation Theorem
arXiv:2109.06953
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.
9 pages. The first 4 sections of this appear will appear separately