Ground state solutions for asymptotically periodic fractional Choquard equations

This paper is dedicated to studying the following fractional Choquard equation (−4) su + V(x)u = �Z RN Q(y)F(u(y)) |x − y| dy Q(x)f(u), u ∈ H s (R N), where s ∈ (0, 1), N ≥ 3, µ ∈ (0, N), V(x) and Q(x) are periodic or asymptotically periodic, and F(t) = R t 0 f(s)ds. By combining the non-Nehari manifold approach with some new inequalities, we establish the existence of Nehari type ground state solutions for the above problem in the periodic and asymptotically periodic cases under mild assumptions on f . Our results generalize and improve the ones in [Y. H. Chen, C. G. Liu, Nonlinearity 29(2016), 1827–1842] and some related literature