Multiplicity of semiclassical solutions for fractional Choquard equations with critical growth

In this article, we focus on the following fractional Choquard equation involving upper critical exponent epsilon(2s)(-Delta)(s)u + V(x)u = epsilon(mu-N) [|x|(-mu)*|u|(2)*(;)(mu,s)]|u|(2)*(-2)(mu,s)u + lambda f(u),x is an element of R-N,where epsilon is a positive parameter,lambda > 0, 0 < s < 1,(-Delta)(s) denotes the fractional Laplacian of order s, N > 2s, 0 < mu < N and 2*(mu,s) is fractional critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality. Under suitable assumptions on the potential V and nonlinearity f, using variational tools from Nehari manifold method and Ljusternik-Schnirelmann category theory, we establish the existence and multiplicity of semiclassical positive solutions.