@Article{JPDE-28-74,
author = {Gluck , Mathew R. and Zhang , Lei},
title = {Classification of Solutions to a Critically Nonlinear System of Elliptic Equations on Euclidean Half-Space},
journal = {Journal of Partial Differential Equations},
year = {2015},
volume = {28},
number = {1},
pages = {74--94},
abstract = {For $N\geq 3$ and non-negative real numbers $a_{ij}$ and $b_{ij}$ ($i,j= 1, \cdots, m$), the semi-linear elliptic system\begin{equation*}
\begin{cases}\Delta u_i+\prod\limits_{j=1}^m u_j^{a_{ij}}=0,\text{in}\mathbb{R}_+^N,\\
\dfrac{\partial u_i}{\partial y_N}=c_i\prod\limits_{j=1}^m u_j^{b_{ij}},\text{on} \partial\mathbb{R}_+^N,\end{cases}\qquad
i=1,\cdots,m,\end{equation*}
%
is considered, where $\mathbb{R}_+^N$ is the upper half of $N$-dimensional Euclidean space. Under suitable assumptions on the exponents $a_{ij}$ and $b_{ij}$, a classification theorem for the positive $C^2(\mathbb{R}_+^N)\cap C^1(\overline{R_+^N})$-solutions of this system is proven.
},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v28.n1.7},
url = {http://global-sci.org/intro/article_detail/jpde/5103.html}
}