Oscillation, suboscillation and nonoscillation criteria for linear systems of ordinary differential equations

TL;DR

This paper develops new criteria for oscillation, suboscillation, and nonoscillation in linear differential systems using Riccati equations and unknown factors, also providing a necessary condition for stability.

Contribution

It introduces novel oscillation and stability criteria for linear ODE systems based on Riccati equations and unknown factors, advancing theoretical understanding.

Findings

Established criteria for oscillation, suboscillation, and nonoscillation.

Derived a necessary condition for Lyapunov stability.

Applied Riccati equation method to linear systems.

Abstract

The Riccati equation method and an approach of the use of unknown factors is used to establish oscillation, suboscillation and nonoscillation criteria for linear systems of ordinary differential equations. A necessary condition for Lyapunov (asymptotic) stability for these systems is obtained.