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 Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 362983 16 pages doi 2009 362983 Research Article Existence and Uniqueness of Solutions for Higher-Order Three-Point Boundary Value Problems Minghe Pei1 and Sung Kag Chang2 1 Department of Mathematics Bei Hua University JiLin 132013 China 2 Department of Mathematics Yeungnam University Kyongsan 712-749 South Korea Correspondence should be addressed to Sung Kag Chang skchang@ Received 5 February 2009 Accepted 14 July 2009 Recommended by Kanishka Perera We are concerned with the higher-order nonlinear three-point boundary value problems xn f t x x . x n-1 n 3 with the three point boundary conditions g x a x a . . x n-1 a 0 xi fb p i 0 1 . n - 3 h x c xfc . xi n-1 l cf 0 where a b c f a c X Rn R -TO TO is continuous g h Rn R are continuous andpi e R i 0 1 . n - 3 are arbitrary given constants. The existence and uniqueness results are obtained by using the method of upper and lower solutions together with Leray-Schauder degree theory. We give two examples to demonstrate our result. Copyright 2009 M. Pei and S. K. Chang. 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. 1. Introduction Higher-order boundary value problems were discussed in many papers in recent years for instance see 1-22 and references therein. However most of all the boundary conditions in the above-mentioned references are for two-point boundary conditions 2-11 14 17-22 and three-point boundary conditions are rarely seen 1 12 13 16 18 . Furthermore works for nonlinear three point boundary conditions are quite rare in literatures. The purpose of this article is to study the existence and uniqueness of solutions for higher order nonlinear three point boundary value problem x n f t x x . x n 1 n 3 2 Boundary Value Problems with nonlinear three point
