Oscillatory and non oscillatory criteria for the systems of two linear first order two by two dimensional matrix ordinary differential equations

TL;DR

This paper develops new integral and interval criteria to determine oscillatory and non-oscillatory solutions of 2x2 linear matrix differential systems using Riccati equations, with comparisons to existing results.

Contribution

It introduces novel oscillatory and non-oscillatory criteria for 2x2 linear matrix systems using Riccati equations, expanding analytical tools in this area.

Findings

Derived integral oscillatory criteria

Established interval oscillatory criteria

Compared one criterion with existing results

Abstract

The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory criteria are obtained. Two non oscillatory criteria are obtained as well. On an example one of the obtained oscillatory criteria is compared with some well known results.