Singular Fractional Choquard Equation with a Critical Nonlinearity and a Radon measure

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.Here, Ω is a bounded domain of R N , s ∈ (0, 1), α, λ and β are positive real parameters, N > 2s, γ ∈ (0, 1), 0 < b < min{N, 4s}, 2 * b = 2N −b N −2s is the critical exponent in the sense of HardyLittlewoodSobolev inequality and µ is a bounded Radon measure in Ω.