Acta mathematica scientia, Series B >
ON CRITICAL SINGULAR QUASILINEAR ELLIPTIC PROBLEM WHEN n=p
Received date: 2003-04-02
Revised date: 2003-11-04
Online published: 2006-04-20
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.
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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