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 ((u − = ∆) 0 su = |u|2∗s−2−εu in in B Rn R \BR, where s ∈ (0,1), (−∆)s is the s-Laplacian, BR is a ball of Rn, 2∗ s := n− 2n 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.