Ground states of a class of gradient systems of Choquard type with general nonlinearity. (December 2021) - Sun, Wei
Abstract: We consider the following gradient system of Choquard type − Δ u 1 + u 1 = ( I μ ∗ F ( u 2 ) ) f ( u 1 ) in R N, − Δ u 2 + u 2 = ( I μ ∗ F ( u 1 ) ) f ( u 2 ) in R N, where N ≥ 3 and I μ ( 0 < μ < N ) is a Riesz potential. By the variational methods, we prove the existence of ground state solutions under the Berestycki–Lions type conditions.