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

CLC Number: 

• 35J65

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