一类次P-Laplace方程非负解的不存在性

数学物理学报 ›› 2009, Vol. 29 ›› Issue (5): 1434-1441.

一类次P-Laplace方程非负解的不存在性

浙江工业大学应用数学系杭州 310032

收稿日期:2007-12-01 修回日期:2009-05-25 出版日期:2009-10-25 发布日期:2009-10-25
基金资助:
出国留学基金(2003833095)和浙江省教育厅重点项目(Z200803357)资助

Nonexistence Results for a Class of Sub-P-Laplacians

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310032

Received:2007-12-01 Revised:2009-05-25 Online:2009-10-25 Published:2009-10-25
Supported by:
出国留学基金(2003833095)和浙江省教育厅重点项目(Z200803357)资助

摘要/Abstract

摘要：

该文得到了在Ω上以下问题

{L_p,_ku+f(u)=0, ,

u|∂Ω=0
非负解的不存在性结果. 其中Ω为Heisenberg型群G中的区域(有界或无界), L_p, _ku=divX (| _X u|^p-2_X u)为对应于Greiner型向量场 X 的一类次P-Laplace算子.

关键词: 不存在性, Heisenberg型群, Pohozaev型恒等式, 次P-Laplace算子

Abstract:

The purpose of the present paper is to establish some nonexistence results of nonnegative solutions for the problem

{L_{p, k} u+f(u)=0, in Ω,
u|∂Ω=0,
where Ω is a domain (bounded or unbounded) in an H-type group G and

L_{p, k} u= div_X (| _X u|^p-2_X u) is a
sub-P-Laplacian associated with Greiner type vector fields X.

Key words: Nonexistence, H-type group, Pohozaev-type identity, Sub-P-Laplacian

中图分类号:

35H99

金永阳. 一类次P-Laplace方程非负解的不存在性[J]. 数学物理学报, 2009, 29(5): 1434-1441.

JIN Yong-Yang. Nonexistence Results for a Class of Sub-P-Laplacians[J]. Acta mathematica scientia,Series A, 2009, 29(5): 1434-1441.

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