On the oscillation of linear matrix Hamiltonian systems

TL;DR

This paper develops new oscillation criteria for linear matrix Hamiltonian systems using Riccati equation methods, extending previous results by relaxing positive definiteness constraints and providing practical examples.

Contribution

It introduces novel oscillation criteria for matrix Hamiltonian systems that do not require positive definiteness of coefficients, expanding the theoretical understanding.

Findings

New oscillation criteria established for matrix Hamiltonian systems.

Extended previous results by removing positive definiteness constraints.

Provided examples demonstrating applicability and comparison of results.

Abstract

The Riccati equation method is used to establish new oscillation criteria for linear matrix Hamiltonian systems. New approaches allow to extend and completed a result, obtained by S. Kumary and S. Umamaheswaram. The oscillation problem for linear matrix Hamiltonian systems in a new direction, which is to break the positive definiteness condition, imposed on one of the coeffcients of the system, is investigated. Some examples are provided for comparing the obtained results with each other and with the result of S. Kumary and S. Umamaheswaram, as well as to illustrate the applicability of these results.