Fractional Kirchhoff Hardy problems with singular and critical Sobolev nonlinearities

The paper deals with the following singular fractional problem {M(integral integral(R2N) vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(N+2s) dxdy) (-Delta)(s)u - mu u/vertical bar x vertical bar(2s) = lambda f(x)u(-gamma) + g(x)u(2s)*(-1) in Omega, u > 0 in Omega, u = 0 in R-nOmega, where Omega subset of R-N is an open bounded domain, with 0 is an element of Omega, dimension N > 2s with s is an element of (0, 1), 2(s)* = 2N/(N - 2s) is the fractional critical Sobolev exponent, lambda and mu are positive parameters, exponent gamma is an element of (0, 1), M models a Kirchhoff coefficient, f is a positive weight while g is a sign-changing function. The main feature and novelty of our problem is the combination of the critical Hardy and Sobolev nonlinearities with the bi-nonlocal framework and a singular nondifferentiable term. By exploiting the Nehari manifold approach, we provide the existence of at least two positive solutions.