Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 659503, 12 pages
doi:10.1155/2011/659503
Research Article

Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems

1College of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
2Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165, China
3Department of Mathematics, Shangqiu Normal University, Shangqiu, Henan 476000, China

Received 26 February 2011; Accepted 3 April 2011

Academic Editor: Mingshu Peng

Copyright © 2011 Yingxin Guo and Junchang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second-order matrix differential system 𝑈 = 𝐴 ( 𝑥 ) 𝑈 + 𝐵 ( 𝑡 ) 𝑉 , 𝑉 = 𝐶 ( 𝑥 ) 𝑈 𝐴 ( 𝑡 ) 𝑉 , where 𝐴 ( 𝑡 ) , 𝐵 ( 𝑡 ) , and 𝐶 ( 𝑡 ) are ( 𝑛 × 𝑛 ) -matrices, and 𝐵 , 𝐶 are Hermitian. These results are sharper than some previous results.