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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 Positive Solutions of a Nonlinear Three-Point Integral Boundary Value Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 519210 11 pages doi 10.1155 2010 519210 Research Article Positive Solutions of a Nonlinear Three-Point Integral Boundary Value Problem Jessada Tariboon1 2 and Thanin Sitthiwirattham1 1 Department of Mathematics Faculty of Applied Science King Mongkut s University of Technology North Bangkok Bangkok 10800 Thailand 2 Centre of Excellence in Mathematics CHE Sri Ayutthaya Road Bangkok 10400 Thailand Correspondence should be addressed to Jessada Tariboon jsdtrb@hotmail.com Received 4 August 2010 Accepted 18 September 2010 Academic Editor Raul F. Manasevich Copyright 2010 J. Tariboon and T. Sitthiwirattham. 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 positive solutions to the three-point integral boundary value problem u a t f u 0 t e 0 1 m 0 0 a f u s ds u 1 where 0 n 1 and 0 a 2 p2. We show the existence of at least one positive solution iff is either superlinear or sublinear by applying the fixed point theorem in cones. 1. Introduction The study of the existence of solutions of multipoint boundary value problems for linear second-order ordinary differential equations was initiated by Il in and Moiseev 1 . Then Gupta 2 studied three-point boundary value problems for nonlinear second-order ordinary differential equations. Since then nonlinear second-order three-point boundary value problems have also been studied by several authors. We refer the reader to 3-19 and the references therein. However all these papers are concerned with problems with three-point boundary condition restrictions on the slope of the solutions and the solutions themselves for example u 0 0 u 0 Pu n u 0 0 u 0 - u O 0 au 0 - u O 0 au fi u 1 au n u 1 au n u 1 au n u 1 u n u 1 0 1.1 and so forth. 2 Boundary Value Problems In this .
