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 \begin{document}$ \begin{cases} (-\Delta)^s u = |u|^{2^*_s-2-\varepsilon}u &\text{in } B_R, \\ u = 0 &\text{in } \mathbb{R}^n \setminus B_R, \end{cases} $\end{document} where \begin{document}$ s \in (0,1) $\end{document} , \begin{document}$ (-\Delta)^s $\end{document} is the s-Laplacian, \begin{document}$ B_R $\end{document} is a ball of \begin{document}$ \mathbb{R}^n $\end{document} , \begin{document}$ 2^*_s : = \frac{2n}{n-2s} $\end{document} is the critical Sobolev exponent and \begin{document}$ \varepsilon>0 $\end{document} is a small parameter. We prove that such solutions have the limit profile of a "tower of bubbles", as \begin{document}$ \varepsilon \to 0^+ $\end{document} , 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.