Existence of three nontrivial solutions for an elliptic system

In this paper we consider the existence of nontrivial solutions for an elliptic system, where the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones and computing the fixed point index in K1, K2 and K1×K2, we obtain that the elliptic system has three nontrivial solutions (u,0), (0,v) and (u∗,v∗). It is remarkable that the third nontrivial solution (u∗,v∗) is established on the Cartesian product of two cones, in which the feature of two equations can be exploited better.