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Báo cáo hóa học: " Research Article Bounded and Periodic Solutions of Semilinear Impulsive Periodic System on Banach Spaces"

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 Bounded and Periodic Solutions of Semilinear Impulsive Periodic System on Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 401947 15 pages doi 10.1155 2008 401947 Research Article Bounded and Periodic Solutions of Semilinear Impulsive Periodic System on Banach Spaces JinRong Wang 1 X. Xiang 1 2 W. Wei 2 and Qian Chen3 1 College of Computer Science and Technology Guizhou University Guiyang Guizhou 550025 China 2 College of Science Guizhou University Guiyang Guizhou 550025 China 3 College of Electronic Science and Information Technology Guizhou University Guiyang Guizhou 550025 China Correspondence should be addressed to JinRong Wang wjr9668@126.com Received 20 February 2008 Revised 6 April 2008 Accepted 7 July 2008 Recommended by Jean Mawhin A class of semilinear impulsive periodic system on Banach spaces is considered. First we introduce the T0-periodic FC-mild solution of semilinear impulsive periodic system. By virtue of Gronwall lemma with impulse the estimate on the PC-mild solutions is derived. The continuity and compactness of the new constructed Poincaré operator determined by impulsive evolution operator corresponding to homogenous linear impulsive periodic system are shown. This allows us to apply Horn s fixed-point theorem to prove the existence of T0-periodic PC-mild solutions when PC-mild solutions are ultimate bounded. This extends the study on periodic solutions of periodic system without impulse to periodic system with impulse on general Banach spaces. At last an example is given for demonstration. Copyright 2008 JinRong Wang 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 It is well known that impulsive periodic motion is a very important and special phenomenon not only in natural science but also in social science such as climate food supplement insecticide population and sustainable development. .