Oscillation and non oscillation criteria for linear nonhomogeneous systems of two first-order ordinary differential equations

TL;DR

This paper develops new oscillation and non-oscillation criteria for nonhomogeneous linear systems of two first-order ODEs using the Riccati equation method, generalizing Wong's criterion.

Contribution

It introduces a Riccati-based approach to establish generalized oscillation criteria for linear systems, extending previous results.

Findings

The oscillation criterion generalizes Wong's criterion.

New non-oscillation criteria are established.

The methods provide a broader understanding of system behavior.

Abstract

The Riccati equation method is used to establish an oscillatory and a non oscillatory criteria for nonhomogeneous linear systems of two first-order ordinary differential equations. It is shown that the obtained oscillatory criterion is a generalization of J. S. W. Wong's oscillatory criterion.