Boundary Value Problems
Volume 2009 (2009), Article ID 273063, 18 pages
Research Article

Positive Solutions for a Class of Coupled System of Singular Three-Point Boundary Value Problems

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

Received 27 February 2009; Accepted 15 May 2009

Academic Editor: Juan J. Nieto

Copyright © 2009 Naseer Ahmad Asif and Rahmat Ali 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.


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(0,1), y′′(t)=g(t,x(t),y(t)), t(0,1), x(0)=y(0)=0, x(1)=αx(η), y(1)=αy(η), is established. The nonlinearities f, g:(0,1)×(0,)×(0,)[0,) are continuous and may be singular at t=0,t=1,x=0, and/or y=0, while the parameters η, α satisfy η(0,1),0<α<1/η. An example is also included to show the applicability of our result.