Fractional nonhomogeneous system with Hardy-Littlewood-Sobolev critical nonlinearity

In this paper, we consider the following fractional elliptic system of Choquard type in R-N (sic)(sic)(sic) where s. (0, 1), N> 2s, 0 < mu < min{N, 4s}, 2* mu = 2N- mu N-2s is the upper critical exponent in the Hardy-Littlewood-Sobolev inequality and f(1), f(2) are nonnegative functionals in the dual space of Ds(RN). When f(1) = f(2) = 0, we establish the uniqueness of the solution to the above problem. On the other hand, when f(1) and f(2) are nonnegative functionals with Ker(f(1)) = Ker(f(2)), the multiplicity of solutions to the above problem is also shown. Moreover, we obtain the global compactness result by using (PS) decomposition.