Differential and Integral Equations

Classifications of nonnegative solutions to some elliptic problems

Yuan Lou and Meijun Zhu

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 29 April 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.


Lou, Yuan; Zhu, Meijun. Classifications of nonnegative solutions to some elliptic problems. Differential Integral Equations 12 (1999), no. 4, 601--612. https://projecteuclid.org/euclid.die/1367267009

Export citation