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Báo cáo hóa học: " Some new nonlinear retarded sum-difference inequalities with applications"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : Some new nonlinear retarded sum-difference inequalities with applications | Wang et al. Advances in Difference Equations 2011 2011 41 http www.advancesindifferenceequations.eom content 2011 1 41 RESEARCH o Advances in Difference Equations a SpringerOpen Journal Open Access Some new nonlinear retarded sum-difference inequalities with applications Wu-Sheng Wang1 Zizun Li2 and Wing-Sum Cheung3 Correspondence wang4896@126. com department of Mathematics Hechi University Guangxi Yizhou 546300 People s Republic of China Full list of author information is available at the end of the article Abstract The main objective of this paper is to establish some new retarded nonlinear sumdifference inequalities with two independent variables which provide explicit bounds on unknown functions. These inequalities given here can be used as handy tools in the study of boundary value problems in partial difference equations. 2000 Mathematics Subject Classification 26D10 26D15 26D20. Keywords sum-difference inequalities boundary value problem 1 Introduction Being important tools in the study of differential integral and integro-differential equations various generalizations of Gronwall inequality 1 2 and their applications have attracted great interests of many mathematicians cf. 3-16 and the references cited therein . Recently Agarwal et al. 3 studied the inequality n u t a t ị gi t s wi u s ds t0 t t1. i 1 bi to Cheung 17 investigated the inequality i 1 x C1 y up x y a p g1 s t uq s t dtds p - q bi xo C1 yo b2 x C2 y p I g2 s t uq s t Ỷ u s t dtds. p - q b2 xo C2 yo Agarwal et al. 18 obtained explicit bounds to the solutions of the following retarded integral inequalities Springer 2011 Wang et al licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Wang et al. Advances in Difference Equations 2011 2011 41 http .