Sign-changing bubble tower solutions for a critical fractional problem

Abstract

In this paper, we consider the following fractional elliptic problem (0.1)(−Δ)su=|u|2s∗−2u,inΩɛ,u=0,inRN∖Ωɛ,where 2s∗=2NN−2s is the critical exponent, 0<s<1, Ωɛ=Ω∖B(0,ɛ) with Ω being a bounded smooth domain in RN containing the origin, N>2s 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.