In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form
⎩⎨⎧u′′=−f(t,v),0<t<1,v′′=−g(t,u),0<t<1u(0)=v(0)=0,ςu(ζ)=u(1),ςv(ζ)=v(1),
where f:(0,1)×[0,+∞)→[0,+∞),g:[0,1]×[0,+∞)→[0,+∞),00, and ςζ<1,f may be singular at t=0 and/or t=1. Under some rather simple conditions, by means of monotone iterative technique, a necessary and sufficient condition for the existence of positive solutions is established, a result on the existence and uniqueness of the positive solution and the iterative sequence of solution is given