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 Singular Multipoint Boundary Value Problems for Systems of Nonlinear | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 978605 22 pages doi 2009 978605 Research Article Positive Solutions of Singular Multipoint Boundary Value Problems for Systems of Nonlinear Second-Order Differential Equations on Infinite Intervals in Banach Spaces Xingqiu Zhang School of Mathematics Liaocheng University Liaocheng Shandong 252059 China Correspondence should be addressed to Xingqiu Zhang zhxq197508@ Received 27 April 2009 Accepted 12 June 2009 Recommended by Donal O Regan The cone theory together with Monch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition an explicit iterative approximation of the solution for the boundary value problem is also derived. Copyright 2009 Xingqiu 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. 1. Introduction In recent years the theory of ordinary differential equations in Banach space has become a new important branch of investigation see . 1-4 and references therein . By employing a fixed point theorem due to Sadovskii Liu 5 investigated the existence of solutions for the following second-order two-point boundary value problems BVP for short on infinite intervals in a Banach space E x t f t x f x f t e J x 0 xQ x to y where f e C JxExE E J 0 to x x limt x t . On the other hand the multipoint boundary value problems arising naturally from applied mathematics and physics have been 2 Boundary Value Problems studied so extensively in scalar case that there are many excellent results about the existence of .