Sign changing bubble tower solutions to a slightly subcritical elliptic problem with non-power nonlinearity

We study the following elliptic problem involving slightly subcritical non-power nonlinearity $$\{\begin{array}{ll}-\mathrm{\Delta }u=\frac{\mathrm{\mid }u{\mathrm{\mid }}^{2^{\ast }-2}u}{[\ln (e+\mathrm{\mid }u\mathrm{\mid }){]}^{\epsilon }}& \mathrm{i}\mathrm{n}\mathrm{\Omega },\\ u=0& \mathrm{o}\mathrm{n}\mathrm{\partial }\mathrm{\Omega },\end{array}$$ where $\mathrm{\Omega }$ is a bounded smooth domain in ${\mathbb{R}}^n$, $n\ge 3$, $2^{\ast }=\frac{2n}{n-2}$ is the critical Sobolev exponent, $\epsilon >0$ is a small parameter. By the finite dimensional Lyapunov-Schmidt reduction method, we construct a sign changing bubble tower solution with the shape of a tower of bubbles as $\epsilon$ goes to zero.