Existence of positive solutions for a singular elliptic problem with critical exponent and measure data

Abstract

We prove the existence of a positive SOLA (Solutions Obtained as Limits of Approximations) to the following PDE involving fractional power of Laplacian ( − Δ ) s u = 1 u γ + λ u 2 s ∗ − 1 + μ in Ω , u > 0 in Ω , u = 0 in ℝ N ∖ Ω . Here, Ω is a bounded domain of ℝN, s∈(0,1), 2s<N, λ,γ∈(0,1), 2s∗=2N∕N−2s is the fractional critical Sobolev exponent and μ is a nonnegative bounded Radon measure in Ω.