tailieunhanh - Báo cáo hóa học: " Research Article A New Singular Impulsive Delay Differential Inequality and Its Application"

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 A New Singular Impulsive Delay Differential Inequality and Its Application | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 461757 13 pages doi 2009 461757 Research Article A New Singular Impulsive Delay Differential Inequality and Its Application Zhixia Ma1 and Xiaohu Wang2 1 College of Computer Science and Technology Southwest University for Nationalities Chengdu 610041 China 2 Yangtze Center of Mathematics Sichuan University Chengdu 610064 China Correspondence should be addressed to Xiaohu Wang xiaohuwang111@ Received 10 January 2009 Accepted 5 March 2009 Recommended by Wing-Sum Cheung A new singular impulsive delay differential inequality is established. Using this inequality the invariant and attracting sets for impulsive neutral neural networks with delays are obtained. Our results can extend and improve earlier publications. Copyright 2009 Z. Ma and X. Wang. 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 inequality technique is an important tool for investigating dynamical behavior of differential equation. The significance of differential and integral inequalities in the qualitative investigation of various classes of functional equations has been fully illustrated during the last 40 years 1-3 . Various inequalities have been established such as the delay integral inequality in 4 the differential inequalities in 5 6 the impulsive differential inequalities in 7-10 Halanay inequalities in 11-13 and generalized Halanay inequalities in 14-17 . By using the technique of inequality the invariant and attracting sets for differential systems have been studied by many authors 9 18-21 . However the inequalities mentioned above are ineffective for studying the invariant and attracting sets of impulsive nonautonomous neutral neural networks with timevarying delays. On the basis of .