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: Research Article On the Existence of Solutions for Dynamic Boundary Value Problems under Barrier Strips Condition | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 378686 9 pages doi 2011 378686 Research Article On the Existence of Solutions for Dynamic Boundary Value Problems under Barrier Strips Condition Hua Luo1 and Yulian An2 1 School of Mathematics and Quantitative Economics Dongbei University of Finance and Economics Dalian 116025 China 2 Department of Mathematics Shanghai Institute of Technology Shanghai 200235 China Correspondence should be addressed to Hua Luo luohuanwnu@ Received 24 November 2010 Accepted 20 January 2011 Academic Editor Jin Liang Copyright 2011 H. Luo and Y. An. 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. By defining a new terminology scatter degree as the supremum of graininess functional value this paper studies the existence of solutions for a nonlinear two-point dynamic boundary value problem on time scales. We do not need any growth restrictions on nonlinear term of dynamic equation besides a barrier strips condition. The main tool in this paper is the induction principle on time scales. 1. Introduction Calculus on time scales which unify continuous and discrete analysis is now still an active area of research. We refer the reader to 1-5 and the references therein for introduction on this theory. In recent years there has been much attention focused on the existence and multiplicity of solutions or positive solutions for dynamic boundary value problems on time scales. See 6-17 for some of them. Under various growth restrictions on nonlinear term of dynamic equation many authors have obtained many excellent results for the above problem by using Topological degree theory fixed-point theorems on cone bifurcation theory and so on. In 2004 Ma and Luo 18 firstly obtained the existence of solutions for the dynamic boundary value .
