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Báo cáo hóa học: " Some nonlinear delay integral inequalities on time scales arising in the theory of dynamics equations"

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: Some nonlinear delay integral inequalities on time scales arising in the theory of dynamics equations | Feng et al. Journal of Inequalities and Applications 2011 2011 29 http www.journalofinequalitiesandapplications.eom content 2011 1 29 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Some nonlinear delay integral inequalities on time scales arising in the theory of dynamics equations Qinghua Feng1 2 Fanwei Meng 1 Yaoming Zhang2 Bin Zheng2 and Jinchuan Zhou2 Correspondence fqhua@sina.com 1School of Mathematical Sciences Qufu Normal University Qufu Shandong 273165 China Full list of author information is available at the end of the article SpringerOpen0 Abstract In this paper some new nonlinear delay integral inequalities on time scales are established which provide a handy tool in the research of boundedness of unknown functions in delay dynamic equations on time scales. The established results generalize some of the results in Lipovan J. Math. Anal. Appl. 322 349-358 2006 Pachpatte J. Math. Anal. Appl. 251 736-751 2000 Li Comput. Math. Appl. 59 1929-1936 2010 and Sun J. Math. Anal. Appl. 301 265-275 2005 . MSC 2010 26E70 26D15 26D10. Keywords delay integral inequality time scales dynamic equation bound 1 Introduction In the 1980s Hilger initiated the concept of time scales 1 which is used as a theory capable to contain both difference and differential calculus in a consistent way. Since then many authors have expounded on various aspects of the theory of dynamic equations on time scales. For example 2-10 and the references therein. In these investigations integral inequalities on time scales have been paid much attention by many authors and a lot of integral inequalities on time scales have been established see 5-10 and the references therein which are designed to unify continuous and discrete analysis and play an important role in the research of boundedness uniqueness stability of solutions of dynamic equations on time scales. But to our knowledge delay integral inequalities on time scales have been paid little attention so far