Normalized ground states to the nonlinear Choquard equations with local perturbations

In this paper, we considered the existence of ground state solutions to the following Choquard equation { -triangle u = lambda u + (I-alpha & lowast; F(u))f(u) + mu|u|(q-2)u in R-N, integral(N)(R)|u|(2)dx = a > 0, where N >= 3, I(alpha )is the Riesz potential of order alpha is an element of (0,N), 2 < q <= 2 + 4/N, mu > 0 and lambda is an element of R is a Lagrange multiplier. Under general assumptions on F is an element of C-1(R,R), for a L-2-subcritical and L-2-criticalof perturbation mu|u|(q-2)u, we established several existence or nonexistence results about the normalized ground state solutions.