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
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
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