EXISTENCE AND CONCENTRATION BEHAVIOR OF GROUND STATE SOLUTIONS FOR MAGNETIC NONLINEAR CHOQUARD EQUATIONS

In the present paper, we consider the following magnetic nonlinear Choquard equation { (-i del + A(x))(2)u) + (g(0()x) + mu g(x))u = (vertical bar x vertical bar(-alpha) * vertical bar u vertical bar(p))vertical bar u vertical bar(p-2)u, {u is an element of H-1 (R-N,R- C) where N >= 3, alpha is an element of (0, N), p is an element of (2 N-alpha/N, 2N-alpha/N-2) A(x) : R-N -> R-N is a magnetic vector potential, mu > 0 is a parameter, g(0)(x) and g(x) are real valued electric potential functions on R-N. Under some suitable conditions, we show that there exists mu* > 0 such that the above equation has at least one ground state solution for mu >= mu*. Moreover, the concentration behavior of solutions is also studied as mu -> +infinity.