tailieunhanh - Báo cáo hoa học: " Research Article Antiperiodic Boundary Value Problem for Second-Order Impulsive Differential Equations on Time Scales"

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 Boundary Value Problem for Second-Order Impulsive Differential Equations on Time Scales | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 567329 14 pages doi 2009 567329 Research Article Antiperiodic Boundary Value Problem for Second-Order Impulsive Differential Equations on Time Scales Yepeng Xing Qiong Wang and De Chen Department of Applied Mathematics Shanghai Normal University Shanghai 200234 China Correspondence should be addressed to Yepeng Xing ypxing-jason@ Received 3 April 2009 Accepted 20 July 2009 Recommended by Alberto Cabada We prove the existence results for second-order impulsive differential equations on time scales with antiperiodic boundary value conditions in the presence of classical fixed point theorems. Copyright 2009 Yepeng Xing 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 and Preliminaries Many evolution processes are characterized by the fact that at certain moments of time they experience a change of state abruptly Consequently it is natural to assume that these perturbations act instantaneously that is in the form of impulses. It is known that many biological phenomena involving threshold bursting rhythm models in medicine and biology optimal control models in economics pharmacokinetics and frequency modulated systems do exhibit impulse effects. The branch of modern applied analysis known as impulsive differential equations provides a natural framework to mathematically describe the aforementioned jumping processes. The reader is referred to monographs 1-4 and references therein for some nice examples and applications to the above areas. The study of dynamic equations on time scales goes back to Stefan Hilger 5 . Now it is still a new area of fairly theoretical exploration in mathematics. In the recent years there has been much progress on the qualitative properties of dynamic systems