TAILIEUCHUNG - Báo cáo: A New Delay Vector Integral Inequality and Its Application

Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010, Article ID 927059, 9 pages doi: Research Article A New Delay Vector Integral Inequality and Its Application Li Xiang,1 Lingying Teng,2 and Hua Wu3 1 2 College of Computer Science, Civil Aviation Flight University of China, Guanghan 618307, China College of Computer Science and Technology, Southwest University for Nationalities, Chengdu 610041, China 3 Civil Aviation Flight University of China, Guanghan 618307, China Correspondence should be addressed to Li Xiang, xiangni sss@ Received 22 September 2010; Accepted 14 December 2010 Academic Editor: Mohamed A. El-Gebeily Copyright q 2010 Li Xiang et al. This is an. | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 927059 9 pages doi 2010 927059 Research Article A New Delay Vector Integral Inequality and Its Application Li Xiang 1 Lingying Teng 2 and Hua Wu3 1 College of Computer Science Civil Aviation Flight University of China Guanghan 618307 China 2 College of Computer Science and Technology Southwest University for Nationalities Chengdu 610041 China 3 Civil Aviation Flight University of China Guanghan 618307 China Correspondence should be addressed to Li Xiang xiangnLsss@ Received 22 September 2010 Accepted 14 December 2010 Academic Editor Mohamed A. El-Gebeily Copyright 2010 Li Xiang 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. A new delay integral inequality is established. Using this inequality and the properties of nonnegative matrix the attracting sets for the nonlinear functional differential equations with distributed delays are obtained. Our results can extend and improve earlier publications. 1. Introduction The attracting set of dynamical systems have been extensively studied over the past few decades and various results are reported. It is well known that one of the most researching tools is inequality technique. With the establishment of various differential and integral inequalities 1-12 the sufficient conditions on the attracting sets for different differential systems are obtained 12-16 . However the inequalities mentioned above are ineffective for studying the attracting sets of a class of nonlinear functional differential equations with distributed delays. Motivated by the above discussions in this paper a new delay vector integral inequality is established. Applying this inequality and the properties of nonnegative matrix some sufficient conditions ensuring the global .

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