# Oscillatory criteria for the hamiltonian systems

## TL;DR

This paper introduces new oscillatory criteria for Hamiltonian systems using the Riccati equation method, notably removing the usual positive definiteness restriction on coefficients, and compares these results with existing criteria.

## Contribution

It presents novel oscillatory criteria for Hamiltonian systems that do not require positive definiteness of coefficients, expanding the applicability of such criteria.

## Key findings

- New oscillatory criteria established for Hamiltonian systems.
- Criteria do not require positive definiteness of coefficients.
- Results compared with existing oscillatory criteria.

## Abstract

The Riccati equation method is used to establish some new oscillatory criteria for the hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of coefficients of the hamiltonian system. The obtained results are compared with some known oscillatory criteria.