Journal of Applied Mathematics
Volume 2012 (2012), Article ID 942042, 13 pages
Research Article

Some Oscillation Results for Linear Hamiltonian Systems

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received 8 September 2011; Accepted 7 December 2011

Academic Editor: Mehmet Sezer

Copyright © 2012 Nan Wang and Fanwei Meng. 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.


The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system 𝑈 = 𝐴 ( 𝑡 ) 𝑈 + 𝐵 ( 𝑡 ) 𝑉 , 𝑉 = 𝐶 ( 𝑡 ) 𝑈 𝐴 ( 𝑡 ) 𝑉 . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the importance of our results.