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Research Article | Open Access

Qualitative properties of stable solutions to some supercritical problems

Yong Liu1, Kelei Wang2, Juncheng Wei3( ), Ke Wu4
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui Province, 230026, China
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei Province, 430072, China
Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada
School of Mathematics and Statistics, Xian Jiaotong University, Xian, Shanxi Province, 710049, China
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Abstract

In this paper, we study symmetry properties of stable solutions to the Lane-Emden equation

Δu+|u|p−1u=0inRn

with n≥11, p in a suitable range and the Liouville equation

Δu+eu=0inRn

with n=10.

Keywords

Lane-Emden equationLiouville equationstable solutionrigidity resultssymmetry

References

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Electronic Research Archive
Volume 30 Issue 5,
May 2022
Pages 1668-1690
DOI: 10.3934/era.2022084

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Cite this article:
Liu Y, Wang K, Wei J, et al. Qualitative properties of stable solutions to some supercritical problems. Electronic Research Archive, 2022, 30(5): 1668-1690. https://doi.org/10.3934/era.2022084

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Received: 06 July 2021
Revised: 14 February 2022
Accepted: 15 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)