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 ´ Antiperiodic Solutions for Lienard-Type Differential Equation with p-Laplacian Operator | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 194824 12 pages doi 2010 194824 Research Article Antiperiodic Solutions for Lienard-Type Differential Equation with p-Laplacian Operator Taiyong Chen Wenbin Liu and Cheng Yang Department of Mathematics China University of Mining and Technology Xuzhou 221008 China Correspondence should be addressed to Taiyong Chen taiyongchen@ Received 2 March 2010 Revised 22 July 2010 Accepted 19 August 2010 Academic Editor Irena Rachủnkova Copyright 2010 Taiyong Chen 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. The existence of antiperiodic solutions for Lienard-type and Duffing-type differential equations with p-Laplacian operator has been studied by using degree theory. The results obtained improve and enrich some known works to some extent. 1. Introduction Antiperiodic problems arise naturally from the mathematical models of various of physical processes see 1 2 and also appear in the study of partial differential equations and abstract differential equations see 3-5 . For instance electron beam focusing system in travelling-wave tube s theories is an antiperiodic problem see 6 . During the past twenty years antiperiodic problems have been studied extensively by numerous scholars. For example for first-order ordinary differential equations a Massera s type criterion was presented in 7 and the validity of the monotone iterative technique was shown in 8 . Moreover for higher-order ordinary differential equations the existence of antiperiodic solutions was considered in 9-12 . Recently existence results were extended to antiperiodic boundary value problems for impulsive differential equations see 13 and antiperiodic wavelets were discussed in 14 . Wang and Li see 15 discussed the existence of solutions of the following
