| Abstract: |
| The purpose of this talk is to construct positive solutions of the semilinear elliptic equation $-\Delta u=u^p$ in ${\mathbb R}^N_+$ with a singular Dirichlet boundary condition.
We show that for $p>(N+1)/(N-1)$ there exists a positive singular solution which behaves like $|x|^{-2/(p-1)}$ as $|x|\to0$ and like the Poisson kernel as $|x|\to\infty$. |
|