# Oscillatory and non oscillatory criteria for linear four dimensional hamiltonian systems

## TL;DR

This paper develops criteria to determine when solutions of four-dimensional linear Hamiltonian systems oscillate or not, using the Riccati equation method, and compares these criteria with existing results.

## Contribution

It introduces new oscillatory and non-oscillatory criteria for four-dimensional Hamiltonian systems using Riccati equations, expanding the theoretical understanding.

## Key findings

- Established an oscillatory criterion for the systems.
- Proved two non-oscillatory criteria.
- Compared the new oscillatory criterion with existing results.

## Abstract

The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of linear four dimensional hamiltonian systems. An oscillatory and two non oscillatory criteria are proved. On an example the obtained oscillatory criterion is compared with some well known results.