Ground state solutions for non-autonomous fractional Choquard equations

We consider the following nonlinear fractional Choquard equation, {(-Delta)(s)u + u = (1 + a(x))(I-alpha * (vertical bar u vertical bar(p)))vertical bar u vertical bar(p-2)u in R-N, {u(x) -> 0 as vertical bar x vertical bar -> infinity, (0.1) here S is an element of (0, 1), alpha is an element of (0, N), p is an element of [2, infinity) and N - 2s/N + alpha < 1/p < N/N + alpha. Assume lim(vertical bar x vertical bar ->infinity) a(x) = 0 and satisfying suitable assumptions but not requiring any symmetry property on a(x), we prove the existence of ground state solutions for (0.1).