关键词: Elliptic equation, Hardy inequality, critical singularity, Mountain Pass Lemma

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.

Key words: Elliptic equation, Hardy inequality, critical singularity, Mountain Pass Lemma