Ground state solutions for fractional Choquard equations involving upper critical exponent

Abstract

In this article, we study the following fractional Choquard equation involving upper critical exponent (−Δ)su+V(x)u=λf(x,u)+[|x|−μ∗|u|2μ,s∗]|u|2μ,s∗−2u,x∈RN, where λ>0, 0<s<1, (−Δ)s denotes the fractional Laplacian of order s, N>2s, 0<μ<2s and 2μ,s∗=2N−μN−2s. When V and f are asymptotically periodic in x, we prove that the equation has a ground state solution for large λ by Nehari method.