A converse of Sturm's separation theorem

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 turning point in the principal part of the equation. Related results are discussed.

Keywords

• sturm separation theorem
• recurrence relations
• sturm separation property
• indefinite principal part
• indefinite leading term