A Liouville theorem for high order degenerate elliptic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Huang, Genggeng^1,2  Li, Congming³ 

[1] Shanghai Jiao Tong Univ, INS, Dept Math, Shanghai 200030, Peoples R China

[2] Shanghai Jiao Tong Univ, MOE LSC, Shanghai 200030, Peoples R China

[3] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA

关键词: Degenerate elliptic;    Moving plane;    Divergence identity;   

DOI  :  10.1016/j.jde.2014.10.017

来源: Elsevier

【 摘 要 】

In this paper, we apply the method of moving plane to the following high order degenerate elliptic equation, (-A)(p)u = u(alpha) in R-+(n+1), n >= 1, where the operator A = y partial derivative(2)(y) + a partial derivative(y) + Delta(x), a >= 1. We get a Liouville theorem for subcritical case and classify the solutions for the critical case. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free