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Exact asymptotic behavior of singular positive solutions of fractional semi-linear elliptic equations


Authors: Hui Yang and Wenming Zou
Journal: Proc. Amer. Math. Soc. 147 (2019), 2999-3009
MSC (2010): Primary 35B09, 35B40, 35J70, 35R11
DOI: https://doi.org/10.1090/proc/14448
Published electronically: March 26, 2019
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Abstract: In this paper, we prove the exact asymptotic behavior of singular positive solutions of fractional semi-linear equations

$\displaystyle (-\Delta )^\sigma u = u^p \textrm { in } B_1\backslash \{0\}$    

with an isolated singularity, where $ \sigma \in (0, 1)$ and $ \frac {n}{n-2\sigma } < p < \frac {n+2\sigma }{n-2\sigma }$.

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Additional Information

Hui Yang
Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China
Email: hui-yang15@mails.tsinghua.edu.cn

Wenming Zou
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: wzou@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/proc/14448
Received by editor(s): June 7, 2018
Received by editor(s) in revised form: August 28, 2018, and October 11, 2018
Published electronically: March 26, 2019
Additional Notes: This research was supported by NSFC
Communicated by: Joachim Krieger
Article copyright: © Copyright 2019 American Mathematical Society