Find in Library

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.