Nodal bubble tower solutions to slightly subcritical elliptic problems with Hardy terms

We study the possible blow-up behavior of solutions to the slightly subcritical elliptic problem with Hardy term $\left\{ \begin{aligned} -Δu-μ\frac{u}{|x|^2} &= |u|^{2^{\ast}-2-\varepsilon}u &&\quad \text{in } Ω, \\\ u &= 0&&\quad \text{on } \partialΩ, \end{aligned} \right.$ in a bounded domain $Ω\subset\mathbb{R}^N (N\ge7)$ with $0\inΩ$, as $μ,\varepsilon\to 0^+$. In \cite{BarGuo-ANS}, we obtained the existence of nodal solutions that blow up positively at the origin and negatively at a different point as $μ=O(ε^α)$ with $α>\frac{N-4}{N-2}$, $\varepsilon\to 0^+$. Here we prove the existence of nodal bubble tower solutions, i.e.\ superpositions of bubbles of different signs, all blowing up at the origin but with different blow-up order, as $μ=O(\varepsilon)$, $\varepsilon\to0^+$.

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