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 for a Class of Coupled System of Singular Three-Point Boundary Value Problem | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 273063 18 pages doi 2009 273063 Research Article Positive Solutions for a Class of Coupled System of Singular Three-Point Boundary Value Problems Naseer Ahmad Asif and Rahmat Ali Khan Centre for Advanced Mathematics and Physics Campus of College of Electrical and Mechanical Engineering National University of Sciences and Technology Peshawar Road Rawalpindi 46000 Pakistan Correspondence should be addressed to Rahmat Ali Khan rahmat_alipk@ Received 27 February 2009 Accepted 15 May 2009 Recommended by Juan J. Nieto Existence of positive solutions for a coupled system of nonlinear three-point boundary value problems of the type -x t f t x t y t t e 0 1 -y t g t x t y t t e 0 1 x 0 y 0 0 x 1 ax n y 1 ay n is established. The nonlinearities f g 0 1 X 0 to X 0 to 0 to are continuous and may be singular at t 0 t 1 x 0 and or y 0 while the parameters n a satisfy n e 0 1 0 a 1 p. An example is also included to show the applicability of our result. Copyright 2009 N. A. Asif and R. A. Khan. 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 Multipoint boundary value problems BVPs arise in different areas of applied mathematics and physics. For example the vibration of a guy wire composed of N parts with a uniform cross-section and different densities in different parts can be modeled as a Multipoint boundary value problem 1 . Many problems in the theory of elastic stability can also be modeled as Multipoint boundary value problem 2 . The study of Multipoint boundary value problems for linear second order ordinary differential equations was initiated by Il in and Moiseev 3 4 and extended to nonlocal linear elliptic boundary value problems by Bitsadze et al. 5 6 . Existence theory for nonlinear three-point .