Nontrivial solutions for nonlinear Schrödinger-Choquard equations with critical exponents

Abstract We study the nonlinear Schrodinger-Choquard equation (0.1) − Δ u + u = I α ∗ | u | p | u | p − 2 u + | u | q − 2 u , x ∈ R N , where N ∈ N , 0 α N , I α denotes Riesz potential. When p = N + α N or p = N + α N − 2 , we get nontrivial solutions under some restrictions on N , q and α respectively. N + α N and N + α N − 2 are lower and upper critical exponents in the sense of the Hardy-Littlewood-Sobolev inequality. This article extend some results of related literatures.