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Let Ω be a bounded smooth domain in   $\mathbb {R}^{N}$   which contains a ball of radius  R  centered at the origin,  N  ≥ 3. Under suitable symmetry assumptions, for each  δ  ∈ (0,  R ), we establish the existence of a sequence ( u   m ,  δ  ) of nodal solutions to the critical problem   $$\begin{align*}-\Delta u=|u|^{2^{\ast}-2}u\text{ in }\Omega_{\delta}:=\{x\in\Omega :\left\vert x\right\vert&gt;\delta\},\quad u=0\text{ on }\partial \Omega_{\delta},\nonumber\end{align*}$$   where   $2^{\ast }:=\frac {2N}{N-2}$   is the critical Sobolev exponent. We show that, if Ω is strictly star-shaped then, for each   $m\in \mathbb {N},$   the solutions  u   m ,  δ   concentrate and blow up at 0, as   $\delta \rightarrow 0,$   and their limit profile is a tower of nodal bubbles, that is, it is a sum of rescaled nonradial sign-changing solutions to the limit problem   $$\begin{align*}-\Delta u=|u|^{2^{\ast}-2}u, \quad u\in D^{1,2}(\mathbb{R}^{N}),\nonumber\end{align*}$$   centered at the origin.

Towers of Nodal Bubbles for the Bahri–Coron Problem in Punctured Domains