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Communications on Pure and Applied Analysis (CPAA)
 

A Liouville type Theorem for an integral system

Pages: 855 - 859, Volume 5, Issue 4, December 2006      doi:10.3934/cpaa.2006.5.855

 
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Dezhong Chen - Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China (email)
Li Ma - Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China (email)

Abstract: In this paper, we study a conjecture of J.Serrin and give a partial generalized result of the work of de Figueiredo and Felmer about Liouville type Theorem for non-negative solutions for an elliptic system. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality.

Keywords:  Liouville theorem, moving plane method, Stein-Weiss inequality.
Mathematics Subject Classification:  35J99, 45E10, 45G05.

Received: December 2005;      Revised: July 2006;      Available Online: September 2006.