Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence of Periodic Solutions for p-Laplacian Equations on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 584375 13 pages doi 2010 584375 Research Article Existence of Periodic Solutions for p-Laplacian Equations on Time Scales Fengjuan Cao 1 Zhenlai Han 1 2 and Shurong Sun1 3 1 School of Science University of Jinan Jinan Shandong 250022 China 2 School of Control Science and Engineering Shandong University Jinan Shandong 250061 China 3 Department of Mathematics and Statistics Missouri University of Science and Technology Rolla mO 65409-0020 USA Correspondence should be addressed to Zhenlai Han hanzhenlai@ Received 30 July 2009 Revised 15 October 2009 Accepted 18 November 2009 Academic Editor A. Pankov Copyright 2010 Fengjuan Cao et al. 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 systematically explore the periodicity of Lienard type p-Laplacian equations on time scales. Sufficient criteria are established for the existence of periodic solutions for such equations which generalize many known results for differential equations when the time scale is chosen as the set of the real numbers. The main method is based on the Mawhin s continuation theorem. 1. Introduction In the past decades periodic problems involving the scalar p-Laplacian were studied by many authors especially for the second-order and three-order p-Laplacian differential equation see 1-8 and the references therein. Of the aforementioned works Lu in 1 investigated the existence of periodic solutions for a p-Laplacian Lienard differential equation with a deviating argument yptyW f y i y i h y t g y t - T t e t ff1 by Mawhin s continuation theorem of coincidence degree theory 3 . The author obtained a new result for the existence of periodic solutions and investigated the relation between the existence of periodic solutions and the deviating .