A generalization of Sturm's comparison theorem

TL;DR

This paper introduces a new comparison theorem for systems of two linear first order ODEs, extending Sturm's comparison theorem using the Riccati equation method and the concept of null-classes.

Contribution

It generalizes Sturm's comparison theorem to systems of equations through a novel approach involving null-classes and Riccati equations.

Findings

Established a new comparison theorem for 2x2 linear systems

Extended Sturm's theorem to more general systems

Introduced the concept of null-classes in differential equations

Abstract

The Riccati equation method is used to establish a new comparison theorem for systems of two linear first order ordinary differential equation. This result is based on a, so called, concept of "null-classes", and is a generalization of Sturm's comparison theorem.