Brief communication. An indefinite Sturm theory

TL;DR

This paper extends Sturm oscillation theory to indefinite systems of even order with Dirichlet boundary conditions, addressing cases with strongly indefinite leading terms, thus broadening the scope of classical Sturm theory.

Contribution

It introduces a Sturm oscillation theorem for indefinite systems of even order with strongly indefinite leading terms, a significant generalization of classical results.

Findings

Established a Sturm oscillation theorem for indefinite systems

Extended classical Sturm theory to strongly indefinite leading terms

Provided theoretical framework for further research in indefinite differential systems

Abstract

Sturm theory for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. Here we propose a Sturm oscillation theorem for indefinite systems of even order and with Dirichlet boundary conditions having strongly indefinite leading term.