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 $$(-Delta)^s u = |u|^2^*_s-2-arepsilonu quad extin B_R,$$ $$u = 0 quad mathbbR^n setminus B_R,$$ where $s in(0,1)$, $(-Delta)^s$ is the s-Laplacian, $B_R$ is a ball of $mathbbR^n$, $2^*_s := rac2nn-2s$ is the critical Sobolev exponent and $arepsilon>0$ is a small parameter. We prove that such solutions have the limit profile of a "tower of bubbles", as $ arepsilon o 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.