Abstract
This article concerns about the existence of a positive SOLA (Solutions Obtained as Limits of Approximations) for the following singular critical Choquard problem involving fractional power of Laplacian and a critical Hardy potential.
(-Delta)(s)u - alpha u/vertical bar x vertical bar(2s) = lambda u + u(-gamma) + beta(integral Omega u(2)b*(y)/vertical bar x-y vertical bar(b)dy)u(2b*-1) + mu in Omega, u > 0 in Omega, u = 0 in R-N\Omega.
Here, Omega is a bounded domain of R-N, s is an element of(0,1), alpha, lambda and beta are positive real parameters, N > 2s, gamma is an element of(0, 1), 0 < b < min{N, 4s}, 2(b)* = 2N - b/N - 2s is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality and mu is a bounded Radon measure in Omega.