Hostname: page-component-68945f75b7-72kh6 Total loading time: 0 Render date: 2024-08-05T18:42:50.560Z Has data issue: false hasContentIssue false
  • English
  • Français

Symmetry of non-negative solutions of a semilinear elliptic equation with singular nonlinearity

Published online by Cambridge University Press:  18 September 2007

Zongming Guo  and
Juncheng Wei
Zongming Guo
Affiliation:
Department of Mathematics, Henan Normal University, Xinxiang 453002, People's Republic of China and Dong Hua University, Shanghai 200051, People's Republic of China (guozm@public.xxptt.ha.cn)
Juncheng Wei
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong (wei@math.cuhk.edu.hk)
Get access Rights & Permissions [Opens in a new window]

Abstract

We use the method of the moving plane (MMP) to obtain necessary and sufficient conditions for the radial symmetry of positive solutions of the following semi-linear elliptic equation with singular nonlinearity:

$$ \Delta u-\frac{1}{u^\nu}=0\quad\text{in~}\mathbb{R}^n,\quad n\geq2, $$

where $\nu>0$. In order to apply the MMP, it is crucial to obtain the asymptotic expansion of $u$ at $\infty$.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 137 , Issue 5 , October 2007 , pp. 963 - 994
Copyright
2007 Royal Society of Edinburgh

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)