Abstract We consider the existence of nontrivial solution u ∈ H 1 (R N) u H^1 (R^N) for the following nonlinear Choquard equation with an almost periodic term − Δ u + u = I μ ∗ (α (y) F (u) ) α (x) f (u) in R N, -u+u= (I ( (y) F (u) ) ) (x) f (u) in R^N, where N ≥ 3, μ ∈ (0, N), I μ is the Riesz potential, F is the primitive function of f, and α is almost periodic. As one will see, almost periodic functions of several variables lack some important features of periodic functions and almost periodic functions on R R. This makes our problem more intriguing and challenging.
Liu et al. (Mon,) studied this question.