Asymptotic behavior of the solution for an elliptic boundary value problem with exponential nonlinearity (Q921251)

The branch of large solutions of the problem \(\Delta u+\lambda e^ u=0\) in \(D\subset {\mathbb{R}}^ n\), \(u=0\) on \(\partial D\) is discussed when \(\lambda\to 0\). The location of the singularities is determined and it depends on the Green's function. The proof uses some a priori bounds for the solutions and a representation formula which is due to Liouville.