A critical fractional choquard problem involving a singular nonlinearity and a radon measure.

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. 0.1 (- Δ) s u - α u | x | 2 s = λ u + u - γ + β ∫ Ω u 2 b ∗ (y) | x - y | b d y u 2 b ∗ - 1 + μ in Ω , u > 0 in Ω , u = 0 in R N \ Ω. <graphic href="11868_2021_382_Article_Equ1.gif"></graphic> Here, Ω is a bounded domain of R N , s ∈ (0 , 1) , α , λ and β are positive real parameters, N > 2 s , γ ∈ (0 , 1) , 0 < b < min { N , 4 s } , 2 b ∗ = 2 N - b N - 2 s is the critical exponent in the sense of Hardy–Littlewood–Sobolev inequality and μ is a bounded Radon measure in Ω . [ABSTRACT FROM AUTHOR]