Positive solutions for singular systems of three-point boundary value problems

This paper investigates the following singular systems of nonlinear second-order three-point boundary value problems {−u″=f(t,v),t∈(0,1),−v″=g(t,u),t∈(0,1),u(0)=v(0)=0,u(1)=αu(η),v(1)=αv(η), where η∈(0,1),0<αη<1η∈(0,1),0<αη<1, ff and gg may be singular at t=0t=0 and/or t=1t=1. Under some weaker conditions the existence of positive solutions is obtained by applying the fixed point theorem of cone expansion and compression. Two examples are then presented to demonstrate the application of our main results.