Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (4): 766-776.

• Articles • Previous Articles     Next Articles

Multiplicity of Solutions for a Singular Equation

 PENG Yan-Fang, WANG Ji-Xiu   

  1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001; School of Mathematics and Computer Science, Xiangfan University, Hubei |Xiangfan 441053
  • Received:2012-08-27 Revised:2013-06-12 Online:2013-08-25 Published:2013-08-25
  • Supported by:

    贵州省科学技术基金(黔科合J字LKS[2011]14号)资助

Abstract:

In this paper, we consider a singular elliptic equation
div(|x|-2au)-μ u/|x|2(1+a)=up-1/|x|bp+λ uq-1/|x|dD.
By virtue of Ekeland variational principle and Mountain  Pass lemma, we prove the equation have multiple positive solutions with a range of the parameters μ and λ.

Key words: Positive solutions, Ekeland , variational principle, Singularity, Caffarelli-Kohn-Nirenberg inequality

CLC Number: 

  • 35J25
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