Ground state solutions of Poholaev type and Nehari type for a class of nonlinear Choquard equations

In this paper, we study the autonomous Choquard equation -Delta u + u = (I-alpha * F(u)) f(u), in R-N , where N >= 3, 0 < alpha < N, I-alpha is a Riesz potential, and f is an element of C(R, R) satisfies the general Berestycki Lions conditions. In Sec. 2, combining constrained variational method with deformation lemma, we obtain a ground state solution of Pohozaev type for the above equation. In Sec. 3, using non-Nehari manifold method, we prove that the above equation has a ground state solution of Nehari type. The results improve some ones in [12]. (C) 2018 Elsevier Inc. All rights reserved.