In this paper, we investigate the asymptotic behavior of local solutions for the semilinear elliptic system $ -\Delta \mathbf{u} = |\mathbf{u}|^{p-1}\mathbf{u} $ with boundary isolated singularity, where $ 1<p<\frac{n+2}{n-2} $, $ n\geq 2 $ and $ \mathbf{u} $ is a $ C^2 $ nonnegative vector-valued function defined on the half space. This work generalizes the correspondence results of Bidaut-Véron-Ponce-Véron on the scalar case, and Ghergu-Kim-Shahgholian on the internal singularity case.
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