We prove the existence of a nontrivial solution u ∈ H¹ (RN) to the nonlinear Choquard equation \[ - Δ u + u = (I_α F (u) ) Fâ (u) {in \(R^N\),} \] where I_α is a Riesz potential, under almost necessary conditions on the nonlinearity F in the spirit of Berestycki and Lions. This solution is a groundstate and has additional local regularity properties; if moreover F is even and monotone on (0,∞ ), then u is of constant sign and radially symmetric.
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