Multiplicity for strongly indefinite semilinear elliptic system

In this paper we study a multiplicity result for a strongly indefinite semilinear elliptic system {−ϵ2Δu+u=g(x)∣v∣q−1vin RN,−ϵ2Δv+v=f(x)∣u∣p−1uin RN. Our interest is the relation between the number of solutions and the topology of the global minima set of a suitable ground energy function.