数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1111-1126.doi: 10.1016/S0252-9602(14)60073-4

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MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

范海宁1,2|刘晓春1   

  1. 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
    2. College of Sciences, China University of Mining and Technology, Xuzhou 221116, China
  • 收稿日期:2013-05-06 修回日期:2013-08-02 出版日期:2014-07-20 发布日期:2014-07-20
  • 基金资助:

    Supported by NSFC (11171261 and 11371282).

MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

 FAN Hai-Ning1,2, LIU Xiao-Chun1   

  1. 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
    2. College of Sciences, China University of Mining and Technology, Xuzhou 221116, China
  • Received:2013-05-06 Revised:2013-08-02 Online:2014-07-20 Published:2014-07-20
  • Supported by:

    Supported by NSFC (11171261 and 11371282).

摘要:

In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.

关键词: Nehari manifold, critical Sobolev exponent, quasi-linear problem, mini-max principle, multiple positive solutions

Abstract:

In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.

Key words: Nehari manifold, critical Sobolev exponent, quasi-linear problem, mini-max principle, multiple positive solutions

中图分类号: 

  • 35J20