Sign-changing bubble tower solutions for a critical fractional problem

In this paper, we consider the following fractional elliptic problem {(-delta)(s)u = |u|(2)(s)(*) (-2)u, in omega(epsilon), (0.1) u = 0, in R-N\omega(epsilon), where 2(s)(*) = 2N/N-2s is the critical exponent, 0 < s < 1, omega(epsilon) = omega\B(0, epsilon) with omega being a bounded smooth domain in R-N containing the origin, N > 2s and B(0, epsilon) is the ball centered at the origin with radius epsilon > 0. We construct a sign-changing solution of (0.1) with the shape of a tower of bubbles as epsilon goes to zero. (C) 2022 Elsevier Ltd. All rights reserved.