Nonradial singular solutions for elliptic equations with exponential nonlinearity

For any $R>0$, infinitely many nonradial singular solutions can be constructed for the following equation:

$$-\mathrm{\Delta }u=e^u\text{in}{B}_R\mathrm{\setminus }\{0\},(0.1)$$

where $B_R=\{x\in {\mathbb{R}}^N(N\ge 3):|x|<R\}$. To construct nonradial singular solutions, we need to consider asymptotic expansion at the isolated singular point $x=0$ of a prescribed solution of (0.1). Then, nonradial singular solutions of (0.1) can be constructed by using the asymptotic expansion and introducing suitable weighted Hölder spaces.