1999 Classifications of nonnegative solutions to some elliptic problems
Yuan Lou, Meijun Zhu
Differential Integral Equations 12(4): 601-612 (1999). DOI: 10.57262/die/1367267009

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 $p, q>1$).

Citation

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Yuan Lou. Meijun Zhu. "Classifications of nonnegative solutions to some elliptic problems." Differential Integral Equations 12 (4) 601 - 612, 1999. https://doi.org/10.57262/die/1367267009

Information

Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1064.35513
MathSciNet: MR1697247
Digital Object Identifier: 10.57262/die/1367267009

Subjects:
Primary: 35J65
Secondary: 35B05

Rights: Copyright © 1999 Khayyam Publishing, Inc.

Vol.12 • No. 4 • 1999
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