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Báo cáo hóa học: " Research Article New Existence Results and Comparison Principles for Impulsive Integral Boundary Value Problem with Lower and Upper Solutions in Reversed Order"

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 New Existence Results and Comparison Principles for Impulsive Integral Boundary Value Problem with Lower and Upper Solutions in Reversed Order | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 783726 13 pages doi 10.1155 2011 783726 Research Article New Existence Results and Comparison Principles for Impulsive Integral Boundary Value Problem with Lower and Upper Solutions in Reversed Order Guotao Wang 1 Lihong Zhang 1 and Guangxing Song2 1 School of Mathematics and Computer Science Shanxi Normal University Linfen Shanxi 041004 China 2 Department of Mathematics China University of Petroleum Qingdao Shandong 266555 China Correspondence should be addressed to Guotao Wang wgt2512@163.com Received 29 December 2010 Accepted 3 March 2011 Academic Editor Jin Liang Copyright 2011 Guotao 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. This paper investigates the existence of the extremal solutions to the integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments under the assumption of existing upper and lower solutions in the reversed order. The sufficient conditions for the existence of solutions were obtained by establishing several new comparison principles and using the monotone iterative technique. At last a concrete example is presented and solved to illustrate the obtained results. 1. Introduction Impulsive differential equations arise naturally from a wide variety of applications such as control theory physics chemistry population dynamics biotechnology industrial robotic and optimal control 1-4 . Therefore it is very important to develop a general theory for differential equations with impulses including some basic aspects of this theory. In this paper we consider the following integral boundary value problem for first-order impulsive functional integrodifferential equations with deviating arguments uft f t u t u a tf Wu t Su tf t 6