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 Infinitely Many Periodic Solutions for Variable Exponent System | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 714179 10 pages doi 2009 714179 Research Article Infinitely Many Periodic Solutions for Variable Exponent Systems Xiaoli Guo 1 Mingxin Lu 2 and Qihu Zhang1 1 Department of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou Henan 450002 China 2 Department of Information Management Nanjing University Nanjing 210093 China Correspondence should be addressed to Qihu Zhang zhangqh1999@ Received 4 December 2008 Accepted 14 April 2009 Recommended by Marta Garcia-Huidobro We mainly consider the system -Ap x u f v h u in R - q x v g u w v in R where 1 p x q x e C1 R are periodic functions and-Ap x u - u pX -2u iscalled p x -Laplacian. We give the existence of infinitely many periodic solutions under some conditions. Copyright 2009 Xiaoli Guo 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. 1. Introduction The study of differential equations and variational problems with variable exponent growth conditions has been a new and interesting topic. Many results have been obtained on this kind of problems for example 1-18 . On the applied background we refer to 1 3 11 18 . In this paper we mainly consider the existence of infinitely many periodic solutions for the system P -Ap x u f v h ù . Áq x v g u viv in R in R where p x q x e C1 R are functions. The operator - p xyu - u p x -2u is called onedimensional p x -Laplacian. Especially if p x p a constant and q x q a constant then P is the well-known constant exponent system. u V is called a solution of P if u v e C1 R u p x -2u and v p x -2v are absolute continuous and satisfy P almost every where. 2 Journal of Inequalities and Applications In 19 the authors consider the existence of positive weak solutions for the .
