Existence of positive solutions for a semilinear elliptic system - Zhang, Zhitao; Cheng, Xiyou (Topological Methods in Nonlinear Analysis, 2011)
In this paper, we are concerned with the existence of (component-wise) positive solutions for a semilinear elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing a cone K_1 × K_2 which is the Cartesian product of two cones in space C(Ω) and computing the fixed point index in K_1 × K_2, we establish the existence of positive solutions for the system. It is remarkable that we deal with our problem on the Cartesian product of two cones, in which the features of two equations can be exploited better.