Semilinear elliptic system with boundary singularity. (English) Zbl 1436.35199
Summary: 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.
MSC:
| 35J91 | Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian |
| 35J47 | Second-order elliptic systems |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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