College of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
Copyright © 2012 Shanliang Zhu and Chunyun Sheng. 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.
We consider the nonlinear dynamic system . We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some examples are included to illustrate the results.