journal6 ›› 2005, Vol. 26 ›› Issue (2): 83-86.

• Mathematics • Previous Articles     Next Articles

Positive Solutions for Singular Critical Elliptic Problems

  

  1. (Department of Mathematics,Zhejiang Normal University,Jinhua 321004,Zhejiang China)
  • Online:2005-04-15 Published:2012-09-22

Abstract: The author deals with the conditions of the existence of the singular elliptic equation -Δpu=|u|r-2u+( |u|p(s)-2u)/(|x|s)+ f(x,u). An analysis on the (P.S.) sequence of the variational functionals corresponding to the equations is given and a local compactness result is obtained.By choosing special Mountain Pass theorem and energy estimate,the author obtains that if  the variational functionals corresponding to the equations satisfy local (P.S.) condition,there exsits a critical point,then the author proves the  exitence of positive solutions.

Key words: singularity, variational method, sobolev embedding, hardy inequality

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