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 ) = α y ( ξ ) , y ( 0 ) = 0 , y ( 1 ) = β x ( η ) , is established. The nonlinearities f , g : ( 0 , 1 ) × [ 0 , ∞ ) × [ 0 , ∞ ) → [ 0 , ∞ ) are continuous and singular at t = 0 , t = 1 , while the parameters α, β, ξ, η satisfy ξ , η ∈ ( 0 , 1 ) , 0 < α β ξ η < 1 . An example is included to show the applicability of our result.