Existence of positive solutions for a second-order ordinary differential system

In this paper we consider the existence of positive solutions for a second-order ordinary differential system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing a cone K1×K2 which is the Cartesian product of two cones in space C[0,1] and computing the fixed point index in K1×K2, we establish the existence of positive solutions for the system. We remark that, differently from the literature, we deal with our problem on the Cartesian product of two cones, in which the feature of two equations can be exploited better.