On semiclassical ground state solutions for Hamiltonian elliptic systems

Abstract

In this paper, we study the following Hamiltonian elliptic system with gradient termfor , where , is a small positive parameter, is a constant vector, and . Suppose that has at least one maximum, we prove that the system has ground state solutions for all sufficiently small . Moreover, we show that these solutions converge to the ground state solutions of the associated limit problem and concentrate to the maxima of in certain sense as .