Articles

ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n=p

  • Yao Yangxin ,
  • Shen Yaotian
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  • School of Mathematical Sciences, South China University of Technology,
    Guangzhou 510640, China

Received date: 2003-04-02

  Revised date: 2003-11-04

  Online published: 2006-04-20

Abstract

This article deals with the problem
$$ -\Lap_p
u=\lambda{|u|^{p-2}u\over\xlnxRt}+f(x,u),\quad x\in\Omega;\qquad
u=0,x\in\partial\Om, $$
where $n = p.$ The authors prove that a Hardy inequality and the constant $ (\pp)^p $ is optimal. They also prove the existence of a nontrivial solution of the above mentioned problem by using the Mountain Pass Lemma.

Cite this article

Yao Yangxin , Shen Yaotian . ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n=p[J]. Acta mathematica scientia, Series B, 2006 , 26(2) : 209 -219 . DOI: 10.1016/S0252-9602(06)60043-X

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