Positive solutions to singular system with four-point coupled boundary conditions

Existence of positive solution to a nonlinear singular system with four-point coupled boundary conditions 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)=0,x(1)=αy(ξ),y(0)=0,y(1)=βx(η), is established. The nonlinearities f,g:(0,1)×[0,∞)×[0,∞)→[0,∞)f,g:(0,1)×[0,∞)×[0,∞)→[0,∞) are continuous and singular at t=0t=0, t=1t=1, while the parameters α, β, ξ, η   satisfy ξ,η∈(0,1)ξ,η∈(0,1), 0<αβξη<10<αβξη<1. An example is included to show the applicability of our result.