Minimal blow-up solutions of mass-critical inhomogeneous Hartree equation

In this paper, we are concerned with the Cauchy problem of the inhomogeneous Hartree equation: iu(t) = -Delta u - k(x)(integral(RN) k(y)/vertical bar x-y vertical bar(2) vertical bar u(t, y)vertical bar(2)dy) u(t, x), x epsilon R-N, N >= 3. First, we establish the mass concentration property of the blow-up solutions. Second, we show that the blow-up solutions with minimal mass should concentrate at a critical point of k. Finally, under certain assumptions on global maximum points of k we establish nonexistence of such solutions. (C) 2013 AIP Publishing LLC.