Positive solutions for singular semi-positone three-point systems

In this paper, we study the existence of positive solutions for a singular semi-positone three-point nonlinear boundary value problem system with parameter λ>0λ>0. Under certain super-linear conditions on the nonlinearities, by using the fixed point index method, we find λ∗>0λ∗>0 such that the three-point boundary value problem system has at least one positive solution for 0<λ<λ∗0<λ<λ∗.