Sign-changing bubble tower solutions for a critical fractional problem. (October 2022) - Chen, Wenjing; Long, Wei; Yang, Jianfu
Abstract: In this paper, we consider the following fractional elliptic problem (0.1) ( − Δ ) s u = | u | 2 s ∗ − 2 u, in Ω ɛ, u = 0, in R N ∖ Ω ɛ, where 2 s ∗ = 2 N N − 2 s is the critical exponent, 0 < s < 1, Ω ɛ = Ω ∖ B ( 0, ɛ ) with Ω being a bounded smooth domain in R N containing the origin, N > 2 s and B ( 0, ɛ ) is the ball centered at the origin with radius ɛ > 0 . We construct a sign-changing solution of (0.1) with the shape of a tower of bubbles as ɛ goes to zero.