Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Multiple Positive Solutions for nth Order Multipoint Boundary Value Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 708376 13 pages doi 2010 708376 Research Article Multiple Positive Solutions for nth Order Multipoint Boundary Value Problem Yaohong Li1 2 and Zhongli Wei2 3 1 Department of Mathematics Suzhou University Suzhou Anhui 234000 China 2 School of Mathematics Shandong University Jinan Shandong 250100 China 3 School of Sciences Shandong Jianzhu University Jinan Shandong 250101 China Correspondence should be addressed to Yaohong Li Received 22 January 2010 Revised 9 April 2010 Accepted 3 June 2010 Academic Editor Ivan T. Kiguradze Copyright 2010 Y. Li and Z. Wei. 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. We study the existence of multiple positive solutions for nth-order multipoint boundary value problem. u it a t f u t 0 t e 0 1 u j-1 0 0 j 1 2 . n - 1 u 1 2m1 aiu where n 2 0 n1 n2 nm 1 a 0 i 1 2 . m. We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature. 1. Introduction The existence of positive solutions for nth-order multipoint boundary problems has been studied by some authors see 1 2 . In 1 Pang et al. studied the expression and properties of Green s funtion and obtained the existence of at least one positive solution for nth-order differential equations by applying means of fixed point index theory u n t a t f u t 0 t e 0 1 m u j-1 0 0 j 1 2 . n - 1 u 1 2 XiAn i 1 where n 2 0 n1 n2 nm 1 ai 0 i 1 2 . m. By using the fixed point theorems of cone expansion and compression of norm type Yang and Wei in 2 also obtained the existence of at least one positive solutions for the BVP if m 2.
