Articles

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

  • FAN Hai-Ning ,
  • LIU Xiao-Chun
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  • 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 date: 2013-05-06

  Revised date: 2013-08-02

  Online published: 2014-07-20

Supported by

Supported by NSFC (11171261 and 11371282).

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.

Cite this article

FAN Hai-Ning , LIU Xiao-Chun . MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1111 -1126 . DOI: 10.1016/S0252-9602(14)60073-4

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