Ground state for Choquard equation with doubly critical growth nonlinearity

摘要

In this paper we consider nonlinear Choquard equation ??u + V(x)u = (Iα ? F(u))f(u) in R N, where V ∈ C(RN), Iα denotes the Riesz potential, f(t) = |t| p?2 t + |t| q?2 t for all t ∈ R, N > 5 and α ∈ (0, N ? 4). Under suitable conditions on V, we obtain that the Choquard equation with doubly critical growth nonlinearity, i.e., p = (N + α)/N, q = (N + α)/(N ? 2), has a nonnegative ground state solution by variational methods.