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: Difference inequality for stability of impulsive difference equations with distributed delays | Li et al. Journal of Inequalities and Applications 2011 2011 8 http content 2011 1 8 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Difference inequality for stability of impulsive difference equations with distributed delays Dingshi Li 1 Shujun Long2 and Xiaohu Wang1 Correspondence lidingshi2006@ xiaohuwang1111@ 1Yangtze Center of Mathematics Sichuan University Chengdu 610064 P. R. China Full list of author information is available at the end of the article SpringerOpen0 Abstract In this paper we consider a class of impulsive difference equations with distributed delays. By establishing an impulsive delay difference inequality and using the properties of p-cone and eigenspace of the spectral radius of non-negative matrices some new sufficient conditions for global exponential stability of the impulsive difference equations with distributed delays are obtained. An example is given to demonstrate the effectiveness of the theory. Keywords Difference equations Impulsive Distributed delays Difference inequality Global exponential stability 1 Introduction Difference equations usually appear in the investigation of systems with discrete time or in the numerical solution of systems with continuous time 1 . In recent years the stability investigation of difference equations has been interesting to many investigators and various advanced results on this problem have been reported 2 3 . However almost all available results have been focused on systems with discrete delays. In reality difference systems with distributed delays become important because it is essential to formulate the discrete-time analogue of the continuous-time system with distributed delays when one wants to simulate or compute the continuous-time one after obtaining its dynamical characteristics. Fortunately such an issue has been addressed in 4-7 . However besides the delay effect an impulsive effect likewise
