tailieunhanh - Báo cáo hóa học: " Gronwall-type integral inequalities with impulses on time scales"

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: Gronwall-type integral inequalities with impulses on time scales | Peng et al. Advances in Difference Equations 2011 2011 26 http content 2011 1 26 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Gronwall-type integral inequalities with impulses on time scales Y Peng1 2 Ying Kang2 Mingxiu Yuan2 Rongfeng Huang2 and Liu Yang2 Correspondence pengyf0803@ 1School of Mathematics and Statistics Wuhan University Wuhan 430072 People s Republic of China Full list of author information is available at the end of the article Springer Abstract In this article some Gronwall-type integral inequalities with impulses on time scales are investigated. Our results extend some known dynamic inequalities on time scales unify and extend some continuous inequalities and their corresponding discrete analogues. Some applications of the main results are given in the end of this article. AMS MOS Subject Classification 34D09 34D99 37M10 35D05 49K25 90C46. Keywords Time scales Integral inequalities Impulse Introduction The theory of time scales which has recently received a lot of attention was initiated by Hilger 1 in his . thesis in 1988 to contain both difference and differential calculus in a consistent way. Since then many authors have investigated the dynamic equations the calculus of variations and the optimal control problem on time scales see 2-11 . At the same time a few papers have studied the theory of integral inequalities on time scales see 12-14 . In this article we study some Gronwall-type integral inequalities on time scales which extend some known dynamic inequalities on time scales unify and extend some continuous inequalities and their corresponding discrete analogues. It is helpful in our result to study dynamic systems and optimal control problem on time scales. Preliminaries For convenience we present some important theorem on time scales in this section. The approach is based on the ideas in 9 and will be of fundamental importance in following results. A .

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