Semilinear elliptic system with boundary singularity

Yimei Li; Jiguang Bao

doi:10.3934/dcds.2020111

Article Contents

2020, Volume 40, Issue 4: 2189-2212. Doi: 10.3934/dcds.2020111

This issue Previous Article Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions Next Article On global smooth solutions of 3-D compressible Euler equations with vanishing density in infinitely expanding balls

Semilinear elliptic system with boundary singularity

Yimei Li and
Jiguang Bao

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received: May 2019

Revised: October 2019

Published: December 2019

The authors are supported in part by the National Natural Science Foundation of China (11631002 and 11871102)

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Abstract

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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Mathematics Subject Classification: 35J61, 35B40, 35B53.

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