Localized semiclassical states for Hamiltonian elliptic systems in dimension two

Abstract

In this paper, we consider the Hamiltonian elliptic system in dimension twowhere V ∈ C(R 2 ) has local minimum points, and f, g ∈ C 1 (R) are assumed to be either superlinear or asymptotically linear at infinity and of subcritical exponential growth in the sense of Trudinger-Moser inequality. Under only a local condition on V , we obtain a family of semiclassical states concentrating around local minimum points of V . In addition, in the case that f and g are superlinear at infinity, the decay and positivity of semiclassical states are also given. The proof is based on a reduction method, variational methods and penalization techniques.