## Differential and Integral Equations

### Classifications of nonnegative solutions to some elliptic problems

#### Abstract

The main purpose of this paper is to show that all nonnegative solutions to $\Delta u = 0$ (or $\Delta u = u^p$) in the n-dimensional upper half space $H = \{ (x', t)| x'\in \Bbb{R}^{n-1}, t>0 \}$ with boundary condition ${\partial u}/{\partial t}= u^q$ on $\partial H$ must be linear functions of $t$ (or $u\equiv 0$) when $n \ge 2$ and $q>1$ (or $n\ge 2$ and $p, q>1$).

#### Article information

Source
Differential Integral Equations, Volume 12, Number 4 (1999), 601-612.

Dates
First available in Project Euclid: 29 April 2013