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 Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 483057 10 pages doi 2011 483057 Research Article Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation Peiguo Zhang Department of Elementary Education Heze University Heze 274000 Shandong China Correspondence should be addressed to Peiguo Zhang pgzhang0509@ Received 19 January 2011 Revised 20 February 2011 Accepted 6 March 2011 Academic Editor Kanishka Perera Copyright 2011 Peiguo Zhang. 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 using the cone theory and the Banach contraction mapping principle the existence and uniqueness results are established for singular third-order boundary value problems. The theorems obtained are very general and complement previous known results. 1. Introduction Third-order differential equations arise in a variety of different areas of applied mathematics and physics such as the deflection of a curved beam having a constant or varying cross section three-layer beam electromagnetic waves or gravity-driven flows 1 . Recently third-order boundary value problems have been studied extensively in the literature see . 213 and their references . In this paper we consider the following third-order boundary value problem u f f t u t 0 t6 0 1 u 0 u 0 0 u 1 au fi where f t x 6 C 0 1 X -TO to -to to 0 n 1. Three-point boundary value problems BVPs for short have been also widely studied because of both practical and theoretical aspects. There have been many papers investigating the solutions of three-point BVPs see 2-5 10 12 and references therein. Recently the existence of solutions of third-order three-point BVP has been studied in 2 3 . Guo et al. 2 show the existence of positive solutions for BVP when 1 a 1 n and 2 Boundary Value .
