Infinitely many nonradial singular solutions of $\mathrm{\Delta }u+e^u=0$ in ${\mathbb{R}}^N\mathrm{\backslash }\{0\}$, $4\le N\le 10$

We construct countably infinitely many nonradial singular solutions of the problem $$\mathrm{\Delta }u+e^u=0\text{ in }{\mathbb{R}}^N\mathrm{\backslash }\{0\},4\le N\le 10$$ of the form $$u(r,\sigma )=-2\log r+\log 2(N-2)+v(\sigma ),$$ where $v(\sigma )$ depends only on $\sigma \in {\mathbb{S}}^{N-1}$. To this end we construct countably infinitely many solutions of $${\mathrm{\Delta }}_{{\mathbb{S}}^{N-1}}v+2(N-2)(e^v-1)=0,4\le N\le 10,$$ using ODE techniques.