The Nehari manifold for a fractional critical Choquard equation involving sign-changing weight functions

In this paper, we prove the existence and multiplicity of nontrivial solutions for the following fractional Choquard equation with critical exponent {(-Delta)(s)u = lambda f(x)vertical bar u vertical bar(q-2u) + g(x) (integral(Omega)vertical bar u vertical bar(2)*(mu,s)/vertical bar x - y vertical bar(mu) dy) vertical bar u vertical bar(2)*(mu,s)(-2)u in Omega u = 0, in R-n \ Omega where Omega is a bounded domain in R-n with smooth boundary, s is an element of (0, 1), 0 < mu < n, n > 2s, 1 < q < 2 and 2*(mu,s) = (2n- mu)/(n-2s) is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality. lambda > 0 is a parameter and f, g : (Omega) over bar -> R are continuous functions but may change sign on Omega. (C) 2018 Elsevier Ltd. All rights reserved.