Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity

摘要

We study the following nonlinear Choquard equation: where 0 < μ < N, N ≥3, V is a continuous real function and F is the primitive function of f. Under some suitable assumptions on the potential V, which include the case V(∞) = 0, that is, V(x) → 0 as |x| → +∞, we prove the existence of a nontrivial solution for the above equation by the penalization method.