Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms

In this paper, we consider the following Schr & ouml;dinger equation with perturbations of Choquard terms: { -Delta u - lambda u = |u|(4)u + mu(I (alpha) *|u|(p))|u|(p-2)u,x is an element of R-3, integral(3)(R)u(2)dx = c, where c > 0, lambda is an element of R, mu is an element of R and I alpha is the Riesz potential with order alpha is an element of (0, 3). The main results in this paper are the following: (1) existence of ground state solution with negative energy for all p is an element of(3+alpha/3,5+alpha/3); (2) existence of mountain-pass solution with positive energy for all p is an element of(3+alpha/3,5+alpha/3); (3) existence of ground state solution forp=5+alpha/3and some p is an element of(5+alpha/3,3+alpha).