On a generalized Sturm theorem

TL;DR

This paper extends the Sturm oscillation theorem to systems of even order with strongly indefinite leading coefficients, broadening its applicability beyond previously studied cases.

Contribution

It introduces a generalized Sturm oscillation theorem specifically for systems of even order with strongly indefinite leading coefficients, a case not covered in prior work.

Findings

Established a Sturm oscillation theorem for even order systems with indefinite leading coefficients.

Extended the classical Sturm theorem to a new class of differential systems.

Provided theoretical foundations for analyzing oscillatory behavior in complex systems.

Abstract

Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of even order having strongly indefinite leading coefficient.