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Liouville-type theorems for polyharmonic equations in $\mathbb{R}^N$ and in $\mathbb{R}^N_+$

Published online by Cambridge University Press:  14 July 2008

Yuxia Guo  and
Jiaquan Liu
Yuxia Guo
Affiliation:
Department of Mathematics, Tsinghua University, Beijing 100084, People's Republic of China
Jiaquan Liu
Affiliation:
LMAM, School of Mathematics, Peking University, Beijing 100871, People's Republic of China (jiaquan@math.pku.edu.cn)
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Abstract

By using the moving plane method combined with integral inequalities and Hardy's inequality, some new Liouville-type theorems for semilinear polyharmonic equations in $\mathbb{R}^N$ and in $\mathbb{R}^N_+$ are proved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 2 , April 2008 , pp. 339 - 359
Copyright
2008 Royal Society of Edinburgh

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