# Oscillation criteria for second order two dimensional linear systems of ordinary differential equations

## TL;DR

This paper develops oscillation criteria for second-order two-dimensional linear systems of ordinary differential equations by leveraging properties of scalar Riccati equations and applying classical theorems.

## Contribution

It introduces new oscillation criteria for these systems based on Riccati equation properties and classical oscillation theorems.

## Key findings

- Established oscillation criteria for second-order systems
- Connected Riccati equation properties to system oscillation
- Provided conditions for global solutions of scalar Riccati equations

## Abstract

Some properties of global solution of scalar Riccati equation are studied. On the basis of these properties using the Whiburn's and Leighton - Nehary's theorems some oscillatory and criteria are proved for second order linear systems of ordinary differential equations.