# zbMATH — the first resource for mathematics

Asymptotic radial symmetry for solutions of $$\Delta u+e^ u=0$$ in a punctured disc. (English) Zbl 0794.35049
Summary: A representation formula for solutions of the equation $\Delta u+2Ke^ u=0,\quad K\text{ a constant}, \tag{*}$ in a punctured disc in terms of multi-valued meromorphic functions is found. As application it is deduced that a necessary and sufficient condition for a solution of $$(*)$$, $$K>0$$, being asymptotic radially symmetric, is $$\int e^ u<\infty$$.

##### MSC:
 35J60 Nonlinear elliptic equations 35C20 Asymptotic expansions of solutions to PDEs 30D30 Meromorphic functions of one complex variable (general theory)
Full Text: