Ground state sign-changing solutions for a class of subcritical Choquard equations with a critical pure power nonlinearity in [formula omitted

Abstract

In this paper, we investigate the existence of ground state sign-changing solutions for a class of Choquard equations −△u+(1+λf(x))u=(Iα∗k|u|p)k(x)|u|p−2u+|u|2∗−2u,x∈RN,where k and f are nonnegative functions, N≥3, 2∗=2NN−2, p∈2,N+αN−2, −λ1<λ<0 and λ1 is the first eigenvalue of the equation −△u+u=λf(x)u in H1(RN). Using the sign-changing Nehari manifold, we prove that the Choquard equation has at least one ground state sign-changing solution. This paper can be regarded as the complementary work of Ghimenti and Van Schaftingen (2016), Van Schaftingen and Xia (2017).