tailieunhanh - báo cáo hóa học: " Some new finite difference inequalities arising in the theory of difference 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 new finite difference inequalities arising in the theory of difference equations | Feng et al. Advances in Difference Equations 2011 2011 21 http content 2011 1 21 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Some new finite difference inequalities arising in the theory of difference equations Qinghua Feng1 2 Fanwei Meng2 and Yaoming Zhang 1 Correspondence fqhua@ 1School of Science Shandong University of Technology Zhangzhou Road 12 Zibo Shandong 255049 China Full list of author information is available at the end of the article SpringerOpen0 Abstract In this work some new finite difference inequalities in two independent variables are established which can be used in the study of qualitative as well as quantitative properties of solutions of certain difference equations. The established results extend some existing results in the literature. MSC 2010 26015 Keywords Finite difference inequalities Difference equations Explicit bounds Qualitative analysis Quantitative analysis 1. Introduction Finite difference inequalities in one or two independent variables which provide explicit bounds play a fundamental role in the study of boundedness uniqueness and continuous dependence on initial data of solutions of difference equations. Many difference inequalities have been established for example see 1-11 and the references therein . In the research of difference inequalities generalization of known inequalities has been paid much attention by many authors. Here we list some recent results in the literature. In 12 Theorems Pachpatte presents the following six discrete inequalities based on which some new bounds on unknown functions are established. m 1 X fli u m n a m n b m n y y c s t u s t s 0 t n 1 Preprint submitted to Advances in Difference Equations June 16 2011 X X a2 u m n a m n b m n y y c s t u s t s m 1 t n 1 m 1 X X a3 u m n a m n y b s n u s n y y c s t u s t s 0 s m 1 t n 1 X XX a4 u m n a m n y b s n u s n y y c s t u s t s m 1 s m 1 t n 1 2011 Feng et .

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