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.

Abstract

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.