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 ellipticsystem, where the nonlinear term is superlinear in one equation andsublinear in the other equation. By constructing a cone $K_1 \timesK_2$ which is the Cartesian product of two cones in space$C(\overline{Ω})$ and computing the fixed point index in $K_1× K_2$, we establish the existence of positive solutions forthe system. It is remarkable that we deal with our problem on theCartesian product of two cones, in which the features of twoequations can be exploited better.