数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 647-662.

• 论文 • 上一篇    下一篇

上半空间积分方程组的Liouville型定理

唐素芳   

  1. 西安财经学院统计学院 西安 710100
  • 收稿日期:2016-10-21 修回日期:2017-01-17 出版日期:2017-08-26 发布日期:2017-08-26
  • 作者简介:唐素芳,E-mail:sufangtang@163.com
  • 基金资助:
    国家自然科学基金(11571268,11572231)

Liouville Type Theorem for an Integral System on a Half Space

Tang Sufang   

  1. School of Statistics, Xi'an University of Finance and Economics, Xi'an 710100
  • Received:2016-10-21 Revised:2017-01-17 Online:2017-08-26 Published:2017-08-26
  • Supported by:
    Supported by the NSFC (11571268, 11572231)

摘要: 该文考虑上半空间一类积分方程组的Liouville型定理.在某些自然结构假设下,利用积分形式的移动球面法和Hardy-Littlewood-Sobolev(HLS)不等式,证明积分方程组正解的不存在性.

关键词: 积分方程组, Liouville型定理, HLS不等式, 移动球面法

Abstract: This paper considers Liouville type theorem for a system of integral equations on the upper half Euclidean space. Under the natural structure conditions, we prove the nonexistence of positive solutions to the system basing on the method of moving sphere in integral form and the Hardy-Littlewood-Sobolev (HLS) inequality.

Key words: Integral system, Liouville theorem, HLS inequality, Moving spheres method

中图分类号: 

  • O175.2