Sign-changing bubble-tower solutions to fractional semilinear elliptic problems

We study the asymptotic and qualitative properties of least energy radial sign- changing solutions to fractional semilinear elliptic problems of the form (−∆)^s u = |u|^{2^*_s−2−ε}u in B_R, u = 0 in R^n B_R, where s ∈ (0,1), (−∆)s is the s-Laplacian, BR is a ball of Rn,2^*_s := {2n}/{n-2s} is the critical Sobolev exponent and ε > 0 is a small parameter. We prove that such solutions have the limit profile of a “tower of bubbles”, as ε → 0+, i.e. the positive and negative parts concentrate at the same point with different concentration speeds. Moreover, we provide information about the nodal set of these solutions.