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 Asymptotic Behavior of Impulsive Inﬁnite Delay Difference Equations with Continuous Variable | Hindawi Publishing Corporation Advances in Difference Equations Volume 2009 Article ID 495972 13 pages doi 2009 495972 Research Article Asymptotic Behavior of Impulsive Infinite Delay Difference Equations with Continuous Variables Zhixia Ma1 and Liguang Xu2 1 College of Computer Science Technology Southwest University for Nationalities Chengdu 610064 China 2 Department of Applied Mathematics Zhejiang University of Technology Hangzhou 310023 China Correspondence should be addressed to Liguang Xu xlg132@ Received 3 June 2009 Accepted 2 August 2009 Recommended by Mouffak Benchohra A class of impulsive infinite delay difference equations with continuous variables is considered. By establishing an infinite delay difference inequality with impulsive initial conditions and using the properties of ọ-cone we obtain the attracting and invariant sets of the equations. Copyright 2009 Z. Ma and L. Xu. 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 Difference equations with continuous variables are difference equations in which the unknown function is a function of a continuous variable 1 . These equations appear as natural descriptions of observed evolution phenomena in many branches of the natural sciences see . 2 3 . The book mentioned in 3 presents an exposition of some unusual properties of difference equations specially of difference equations with continuous variables. In the recent years the asymptotic behavior and other behavior of delay difference equations with continuous variables have received much attention due to its potential application in various fields such as numerical analysis control theory finite mathematics and computer science. Many results have appeared in the literatures see for example 1 4-7 . However besides the delay effect an impulsive effect likewise .