Semiclassical limits of ground states for Hamiltonian elliptic system with gradient term

In this paper, we study the following Hamiltonian elliptic system with gradient term {-epsilon(2)Delta psi + epsilon(b) over bar . del psi + psi + V(x)phi = Sigma(I)(i+1) K-i(x)vertical bar eta vertical bar(pi-2)phi in R-N, -epsilon(2)Delta phi + epsilon(b) over bar . del phi + phi + V(x)psi = Sigma(I)(i+1) K-i(x)vertical bar eta vertical bar(pi-2)psi in R-N, where eta = (psi, phi) : R-N -> R-2, V, K-i is an element of C(R-N,R), epsilon > 0 is a small parameter and b is a constant vector. Suppose that V is sign-changing and has at least one global minimum, and K-i has at least one global maximum. We prove that there are two families of semiclassical solutions, for sufficiently small epsilon, with the least energy, one concentrating on the set of minimal points of V and the other on the set of maximal points of K-i. Moreover, the convergence and exponential decay of semiclassical solutions are also explored. (C) 2017 Published by Elsevier Ltd.