Boundary Value Problems
Volume 2009 (2009), Article ID 273063, 18 pages
doi:10.1155/2009/273063

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

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.