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›› 2009, Vol. 26 ›› Issue (2): 158-166.DOI: 10.7523/j.issn.2095-6134.2009.2.003

• Research Articles • Previous Articles     Next Articles

Positive solutions for semilinear elliptic equations with critical Sobolev exponents

GUO Qian-Qiao, CUI Xue-Wei   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China
  • Received:2008-02-27 Revised:2008-07-17 Online:2009-03-15
  • Supported by:

    supported by Natural Science Basic Research Plan in Shaanxi Province of China(2006A09) 

Abstract:

We consider the following semilinear elliptic equation - Δ u-μ u |x|2 =g(x,u)+|u|2*-2u in Ω with Dirichlet boundary condition, where g(x,·) has subcritical growth at infinity. The existence of positive solutions are obtained by variational method in the spirit of Brézis-Nirenberg.

Key words: critical Sobolev exponents, Hardy potentials, mountain pass lemma

CLC Number: