Differential and Integral Equations

Classifications of nonnegative solutions to some elliptic problems

Yuan Lou and Meijun Zhu

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.die/1367267009

Mathematical Reviews number (MathSciNet)
MR1697247

Zentralblatt MATH identifier
1064.35513

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

Citation

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


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