A GENERALIZATION OF STURM’S COMPARISON THEOREM

Gevorg A. Grigorian

doi:10.1216/rmj.2023.53.1807

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 the concept of “null-classes”, and is a generalization of Sturm’s comparison theorem.

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Gevorg A. Grigorian. "A GENERALIZATION OF STURM’S COMPARISON THEOREM." Rocky Mountain J. Math. 53 (6) 1807 - 1815, December 2023. https://doi.org/10.1216/rmj.2023.53.1807

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Received: 25 November 2021; Revised: 27 July 2022; Accepted: 27 July 2022; Published: December 2023

First available in Project Euclid: 21 December 2023

MathSciNet: MR4682743

zbMATH: 07784575

Digital Object Identifier: 10.1216/rmj.2023.53.1807

Subjects:

Primary: 34C10

Secondary: 34C99

Keywords: Linear systems , null-classes , null-elements , Riccati equation , Sturm’s comparison theorem , Sturm’s majorant (minorant)

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