Existence and multiplicity of solutions for fractional Choquard equations

We consider the following fractional order Choquard equation (−△)α∕2u(x)+(λV(x)−β)u=(|x|−μ∗|u|2μ∗)|u|2μ∗−2u,x∈Rn,with the nonlinearity in the critical growth, where α∈(0,2), n≥3, λ,β∈R+ and 2μ∗=(2n−μ)∕(n−α). Using the variational method, we establish the existence and multiplicity of weak solutions.