On singular perturbations of superlinear elliptic systems

We study the existence, multiplicity and shape of positive solutions of the system − ε 2 Δ u + V ( x ) u = K ( x ) g ( v ) , − ε 2 Δ v + V ( x ) v = H ( x ) f ( u ) in R N , as ε → 0 . The functions f and g are power-like nonlinearities with superlinear and subcritical growth at infinity, and V, H, K are positive and locally Hölder continuous.