数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (5): 1619-1633.doi: 10.1016/S0252-9602(14)60108-9

• 论文 • 上一篇    下一篇

ON POSITIVE G-SYMMETRIC SOLUTIONS OF A WEIGHTED QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL HARDY-SOBOLEV EXPONENT

邓志颖*, 黄毅生   

  1. School of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; Department of Mathematics, Soochow University, Suzhou 215006, China
  • 收稿日期:2012-12-10 修回日期:2013-11-09 出版日期:2014-09-20 发布日期:2014-09-20
  • 通讯作者: 邓志颖,dengzy@cqupt.edu.cn E-mail:dengzy@cqupt.edu.cn;yishengh@suda.edu.cn
  • 基金资助:

    Supported by the Natural Science Foundation of China (11071180; 11171247), and Project supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ130503).

ON POSITIVE G-SYMMETRIC SOLUTIONS OF A WEIGHTED QUASILINEAR ELLIPTIC EQUATION WITH CRITICAL HARDY-SOBOLEV EXPONENT

 DENG Zhi-Ying*, HUANG Yi-Sheng   

  1. School of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China; Department of Mathematics, Soochow University, Suzhou 215006, China
  • Received:2012-12-10 Revised:2013-11-09 Online:2014-09-20 Published:2014-09-20
  • Contact: DENG Zhi-Ying,dengzy@cqupt.edu.cn E-mail:dengzy@cqupt.edu.cn;yishengh@suda.edu.cn
  • Supported by:

    Supported by the Natural Science Foundation of China (11071180; 11171247), and Project supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ130503).

摘要:

In this paper, we are concerned with a weighted quasilinear elliptic equation involving critical Hardy–Sobolev exponent in a bounded G-symmetric domain. By using the symmetric criticality principle of Palais and variational method, we establish several existence and multiplicity results of positive G-symmetric solutions under certain appropriate
hypotheses on the potential and the nonlinearity.

关键词: G-symmetric solution, symmetric criticality principle, critical Hardy–Sobolev exponent, quasilinear elliptic equation

Abstract:

In this paper, we are concerned with a weighted quasilinear elliptic equation involving critical Hardy–Sobolev exponent in a bounded G-symmetric domain. By using the symmetric criticality principle of Palais and variational method, we establish several existence and multiplicity results of positive G-symmetric solutions under certain appropriate
hypotheses on the potential and the nonlinearity.

Key words: G-symmetric solution, symmetric criticality principle, critical Hardy–Sobolev exponent, quasilinear elliptic equation

中图分类号: 

  • 35B33