Special Session 101: 

Positive solutions of a semilinear elliptic equation with singular Dirichlet boundary data

Tatsuki Kawakami
Ryukoku University
Japan
Co-Author(s):    Marek Fila and Kazuhiro Ishige
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 $|x|\to\infty$.