Key points are not available for this paper at this time.
The aim of this paper is to deal with the non-local fractional counterpart of the Laplace equation involving critical non-linearities studied in the famous paper of Brezis and Nirenberg (1983). Namely, our model is the equation \ (− Δ) s u − λ u = | u | 2 ∗ − 2 u a m p ; in Ω, u = 0 a m p ; in R n ∖ Ω, \{ {arrayll (-) ˢ u- u=|u|^2^*-2u & { in }, \\ u=0 & { in } Rⁿ \, , array. \ where (− Δ) s (-) ˢ is the fractional Laplace operator, s ∈ (0, 1) s (0, 1), Ω is an open bounded set of
Servadei et al. (Mon,) studied this question.