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

作者：Fan, Haining^*; Liu, Xiaochun

来源：Acta Mathematica Scientia, 2014, 34(4): 1111-1126.

DOI：10.1016/S0252-9602(14)60073-4

• Nehari manifold
• critical Sobolev exponent
• quasi-linear problem
• mini-max principle
• multiple positive solutions

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.

• 出版日期2014-7
• 单位武汉大学; 中国矿业大学（北京）